This is what the Catechism of the Catholic Church states on this issue:
The Lord's day
1166 "By a tradition handed down from the apostles which took its origin from the very day of Christ's Resurrection, the Church celebrates the Paschal mystery every seventh day, which day is appropriately called the Lord's Day or Sunday." (Vatican II, Sacrosanctum Concilium 106) The day of Christ's Resurrection is both the first day of the week, the memorial of the first day of creation, and the "eighth day," on which Christ after his "rest" on the great sabbath inaugurates the "day that the Lord has made," the "day that knows no evening." (Byzantine liturgy) The Lord's Supper is its center, for there the whole community of the faithful encounters the risen Lord who invites them to his banquet: (cf. John 21:12; Luke 24:30)
The Lord's day, the day of Resurrection, the day of Christians, is our day. It is called the Lord's day because on it the Lord rose victorious to the Father. If pagans call it the "day of the sun," we willingly agree, for today the light of the world is raised, today is revealed the sun of justice with healing in his rays.
St. Jerome, Pasch.: Corpus Christianorum, Series Latina 78,550
1167 Sunday is the pre-eminent day for the liturgical assembly, when the faithful gather "to listen to the word of God and take part in the Eucharist, thus calling to mind the Passion, Resurrection, and glory of the Lord Jesus, and giving thanks to God who 'has begotten them again, by the resurrection of Jesus Christ from the dead' unto a living hope": (Vatican II, Sacrosanctum Concilium 106)
When we ponder, O Christ, the marvels accomplished on this day, the Sunday of your holy resurrection, we say: "Blessed is Sunday, for on it began creation . . . the world's salvation . . . the renewal of the human race. . . . On Sunday Heaven and earth rejoiced and the whole universe was filled with light. Blessed is Sunday, for on it were opened the gates of paradise so that Adam and all the exiles might enter it without fear.
Fanqith, The Syriac Office of Antioch, vol. VI, first part of Summer, 193 B
The liturgical year
1168 Beginning with the Easter Triduum as its source of light, the new age of the Resurrection fills the whole liturgical year with its brilliance. Gradually, on either side of this source, the year is transfigured by the liturgy. It really is a "year of the Lord's favor." (Luke 4:19) The economy of salvation is at work within the framework of time, but since its fulfillment in the Passover of Jesus and the outpouring of the Holy Spirit, the culmination of history is anticipated "as a foretaste," and the kingdom of God enters into our time.
1169 Therefore Easter is not simply one feast among others, but the "Feast of feasts," the "Solemnity of solemnities," just as the Eucharist is the "Sacrament of sacraments" (the Great Sacrament). St. Athanasius calls Easter "the Great Sunday" (St. Athanasius (ad 329) ep. fest. 1:PG 24,1366) and the Eastern Churches call Holy Week "the Great Week." The mystery of the Resurrection, in which Christ crushed death, permeates with its powerful energy our old time, until all is subjected to him.
1170 At the Council of Nicaea in 325, all the Churches agreed that Easter, the Christian Passover, should be celebrated on the Sunday following the first full moon (14 Nisan) after the vernal equinox. Because of the different methods of calculating the 14th day of the month of Nisan, the date of Easter in the Western and Eastern Churches is not always the same. For this reason, the Churches are currently seeking an agreement in order once again to celebrate the day of the Lord's Resurrection on a common date.
1171 In the liturgical year the various aspects of the one Paschal mystery unfold. This is also the case with the cycle of feasts surrounding the mystery of the incarnation (Annunciation, Christmas, Epiphany). They commemorate the beginning of our salvation and communicate to us the first fruits of the Paschal mystery.
The sanctoral in the liturgical year
1172 "In celebrating this annual cycle of the mysteries of Christ, Holy Church honors the Blessed Mary, Mother of God, with a special love. She is inseparably linked with the saving work of her Son. In her the Church admires and exalts the most excellent fruit of redemption and joyfully contemplates, as in a faultless image, that which she herself desires and hopes wholly to be." (Vatican II, Sacrosanctum Concilium 103)
1173 When the Church keeps the memorials of martyrs and other saints during the annual cycle, she proclaims the Paschal mystery in those "who have suffered and have been glorified with Christ. She proposes them to the faithful as examples who draw all men to the Father through Christ, and through their merits she begs for God's favors." (Vatican II, Sacrosanctum Concilium 104, 108, and 111)
In Brief
1193 Sunday, the "Lord's Day," is the principal day for the celebration of the Eucharist because it is the day of the Resurrection. It is the pre-eminent day of the liturgical assembly, the day of the Christian family, and the day of joy and rest from work. Sunday is "the foundation and kernel of the whole liturgical year". (Vatican II, Sacrosanctum Concilium 106)
1194 The Church, "in the course of the year, . . . unfolds the whole mystery of Christ from his Incarnation and Nativity through his Ascension, to Pentecost and the expectation of the blessed hope of the coming of the Lord". (Vatican II, Sacrosanctum Concilium 102 § 2)
1195 By keeping the memorials of the saints - first of all the holy Mother of God, then the apostles, the martyrs, and other saints - on fixed days of the liturgical year, the Church on earth shows that she is united with the liturgy of Heaven. She gives glory to Christ for having accomplished his salvation in his glorified members; their example encourages her on her way to the Father.
The day of the Resurrection: the new creation
2174 Jesus rose from the dead "on the first day of the week." (cf. Matthew 28:1; Mark 16:2; Luke 24:1; John 20:1) Because it is the "first day," the day of Christ's Resurrection recalls the first creation. Because it is the "eighth day" following the sabbath, (cf. Mark 16:1; Matthew 28:1) it symbolizes the new creation ushered in by Christ's Resurrection. For Christians it has become the first of all days, the first of all feasts, the Lord's Day (he kuriake hemera, dies dominica) Sunday:
We all gather on the day of the sun, for it is the first day [after the Jewish sabbath, but also the first day] when God, separating matter from darkness, made the world; and on this same day Jesus Christ our Savior rose from the dead.
St. Justin, I Apol. 67:PG 6,429 and 432
Sunday - fulfillment of the sabbath
2175 Sunday is expressly distinguished from the sabbath which it follows chronologically every week; for Christians its ceremonial observance replaces that of the sabbath. In Christ's Passover, Sunday fulfills the spiritual truth of the Jewish sabbath and announces man's eternal rest in God. For worship under the Law prepared for the mystery of Christ, and what was done there prefigured some aspects of Christ: (cf. 1 Corinthians 10:11)
Those who lived according to the old order of things have come to a new hope, no longer keeping the sabbath, but the Lord's Day, in which our life is blessed by him and by his death. (St. Ignatius of Antioch, Ad Magn. 9,1: SCh 10, 88)
2176 The celebration of Sunday observes the moral commandment inscribed by nature in the human heart to render to God an outward, visible, public, and regular worship "as a sign of his universal beneficence to all." (St. Thomas Aquinas, STh II-II,122,4) Sunday worship fulfills the moral command of the Old Covenant, taking up its rhythm and spirit in the weekly celebration of the Creator and Redeemer of his people.
The Sunday Eucharist
2177 The Sunday celebration of the Lord's Day and his Eucharist is at the heart of the Church's life. "Sunday is the day on which the paschal mystery is celebrated in light of the apostolic tradition and is to be observed as the foremost holy day of obligation in the universal Church." (Code of Canon Law, canon 1246 § 1) "Also to be observed are the day of the Nativity of Our Lord Jesus Christ, the Epiphany, the Ascension of Christ, the feast of the Body and Blood of Christi, the feast of Mary the Mother of God, her Immaculate Conception, her Assumption, the feast of Saint Joseph, the feast of the Apostles Saints Peter and Paul, and the feast of All Saints." (Code of Canon Law, canon 1246 § 2): "The conference of bishops can abolish certain holy days of obligation or transfer them to a Sunday with prior approval of the Apostolic See."
2178 This practice of the Christian assembly dates from the beginnings of the apostolic age. (cf. Acts 2:42-46; 1 Corinthians 11:17) The Letter to the Hebrews reminds the faithful "not to neglect to meet together, as is the habit of some, but to encourage one another." (Hebrews 10:25)
Tradition preserves the memory of an ever-timely exhortation: Come to Church early, approach the Lord, and confess your sins, repent in prayer. . . . Be present at the sacred and divine liturgy, conclude its prayer and do not leave before the dismissal. . . . We have often said: "This day is given to you for prayer and rest. This is the day that the Lord has made, let us rejoice and be glad in it."
Sermo de die dominica 2 et 6:PG 86/1,416C and 421C
2179 "A parish is a definite community of the Christian faithful established on a stable basis within a particular church; the pastoral care of the parish is entrusted to a pastor as its own shepherd under the authority of the diocesan bishop." (Code of Canon Law, canon 515 § 1) It is the place where all the faithful can be gathered together for the Sunday celebration of the Eucharist. The parish initiates the Christian people into the ordinary expression of the liturgical life: it gathers them together in this celebration; it teaches Christ's saving doctrine; it practices the charity of the Lord in good works and brotherly love:
You cannot pray at home as at church, where there is a great multitude, where exclamations are cried out to God as from one great heart, and where there is something more: the union of minds, the accord of souls, the bond of charity, the prayers of the priests.
St. John Chrysostom, De incomprehensibili 3,6:PG 48,725
The Sunday obligation
2180 The precept of the Church specifies the law of the Lord more precisely: "On Sundays and other holy days of obligation the faithful are bound to participate in the Mass." (Code of Canon Law, canon 1247) "The precept of participating in the Mass is satisfied by assistance at a Mass which is celebrated anywhere in a Catholic rite either on the holy day or on the evening of the preceding day." (Code of Canon Law, canon 1248 § 1)
2181 The Sunday Eucharist is the foundation and confirmation of all Christian practice. For this reason the faithful are obliged to participate in the Eucharist on days of obligation, unless excused for a serious reason (for example, illness, the care of infants) or dispensed by their own pastor. (cf. Code of Canon Law, canon 1245) Those who deliberately fail in this obligation commit a grave sin.
2182 Participation in the communal celebration of the Sunday Eucharist is a testimony of belonging and of being faithful to Christ and to his Church. The faithful give witness by this to their communion in faith and charity. Together they testify to God's holiness and their hope of salvation. They strengthen one another under the guidance of the Holy Spirit.
2183 "If because of lack of a sacred minister or for other grave cause participation in the celebration of the Eucharist is impossible, it is specially recommended that the faithful take part in the Liturgy of the Word if it is celebrated in the parish church or in another sacred place according to the prescriptions of the diocesan bishop, or engage in prayer for an appropriate amount of time personally or in a family or, as occasion offers, in groups of families." (Code of Canon Law, canon 1248 § 2)
A day of grace and rest from work
2184 Just as God "rested on the seventh day from all his work which he had done," (Genesis 2:2) human life has a rhythm of work and rest. The institution of the Lord's Day helps everyone enjoy adequate rest and leisure to cultivate their familial, cultural, social, and religious lives. (cf. Vatican II, Gaudium et spes 67 § 3)
2185 On Sundays and other holy days of obligation, the faithful are to refrain from engaging in work or activities that hinder the worship owed to God, the joy proper to the Lord's Day, the performance of the works of mercy, and the appropriate relaxation of mind and body. (cf. Code of Canon Law, canon 120) Family needs or important social service can legitimately excuse from the obligation of Sunday rest. The faithful should see to it that legitimate excuses do not lead to habits prejudicial to religion, family life, and health.
The charity of truth seeks holy leisure — the necessity of charity accepts just work.
St. Augustine, De civ. Dei 19,19:PL 41,647
2186 Those Christians who have leisure should be mindful of their brethren who have the same needs and the same rights, yet cannot rest from work because of poverty and misery. Sunday is traditionally consecrated by Christian piety to good works and humble service of the sick, the infirm, and the elderly. Christians will also sanctify Sunday by devoting time and care to their families and relatives, often difficult to do on other days of the week. Sunday is a time for reflection, silence, cultivation of the mind, and meditation which furthers the growth of the Christian interior life.
2187 Sanctifying Sundays and holy days requires a common effort. Every Christian should avoid making unnecessary demands on others that would hinder them from observing the Lord's Day. Traditional activities (sport, restaurants, etc.), and social necessities (public services, etc.), require some people to work on Sundays, but everyone should still take care to set aside sufficient time for leisure. With temperance and charity the faithful will see to it that they avoid the excesses and violence sometimes associated with popular leisure activities. In spite of economic constraints, public authorities should ensure citizens a time intended for rest and divine worship. Employers have a similar obligation toward their employees.
2188 In respecting religious liberty and the common good of all, Christians should seek recognition of Sundays and the Church's holy days as legal holidays. They have to give everyone a public example of prayer, respect, and joy and defend their traditions as a precious contribution to the spiritual life of society. If a country's legislation or other reasons require work on Sunday, the day should nevertheless be lived as the day of our deliverance which lets us share in this "festal gathering," this "assembly of the firstborn who are enrolled in Heaven." (Hebrews 12:22-23)
In Brief
2189 "Observe the sabbath day, to keep it holy." (Deuteronomy 5:12) "The seventh day is a sabbath of solemn rest, holy to the Lord." (Exodus 31:15)
2190 The sabbath, which represented the completion of the first creation, has been replaced by Sunday which recalls the new creation inaugurated by the Resurrection of Christ.
2191 The Church celebrates the day of Christ's Resurrection on the "eighth day," Sunday, which is rightly called the Lord's Day. (cf. Vatican II, Sacrosanctum Concilium 106)
2192 "Sunday . . . is to be observed as the foremost holy day of obligation in the universal Church". (Code of Canon Law, canon 1246 § 1) "On Sundays and other holy days of obligation the faithful are bound to participate in the Mass". (Code of Canon Law, canon 1247)
2193 "On Sundays and other holy days of obligation the faithful are bound . . . to abstain from those labors and business concerns which impede the worship to be rendered to God, the joy which is proper to the Lord's Day, or the proper relaxation of mind and body." (Code of Canon Law, canon 1247)
2194 The institution of Sunday helps all "to be allowed sufficient rest and leisure to cultivate their familial, cultural, social, and religious lives." (Vatican II, Gaudium et spes 67 § 3)
2195 Every Christian should avoid making unnecessary demands on others that would hinder them from observing the Lord's Day.
- — St. Ignatius of Antioch, (A.D. 50-107)
— The Didache, (A.D. 80-90)
— Didascalia (Apostolorum), (composed A.D. c.230)
— Eusebius of Cæsarea, (A.D. c.263-338)
— St. Victorinus, (A.D. 260-303)
— The Apostolic Constitutions (or Constitutions of the Holy Apostles), (dated A.D.c 270)
— St. Athanasius of Alexandria, (A.D. 296-372)
— St. Cyril of Jerusalem, (A.D. 315-386)
— St. Jerome, (A.D. 342-420)
— St. John Chrysostom, (A.D. 344 - 407)
— The Byzantine Liturgy, (prior A.D. 379)
St. Ignatius of Antioch, (A.D. 50-107), Syrian; ecclesiastical writer, bishop, martyr. A disciple of St. John, the Apostle; he was bishop of Antioch, in which see he succeeded St. Peter, or, as others think, Evodius. He is supposed to have governed that church for about forty years. He suffered martyrdom at Rome in the year 107.
[T]hose who were brought up in the ancient order of things [i.e., Jews] have come to the possession of a new hope, no longer observing the Sabbath, but living in the observance of the Lord's day, on which also our life has sprung up again by him and by his death.
Letter to the Magnesians 8 [A.D. 110]
The Didache, (A.D. 80-90) the Teaching of the Twelve Apostles (Didache means "Teaching") is a brief early Christian treatise, dated by most scholars to the late first or early 2nd century.
But every Lord's day . . . gather yourselves together and break bread, and give thanksgiving after having confessed your transgressions, that your sacrifice may be pure. But let no one that is at variance with his fellow come together with you until they be reconciled, that your sacrifice may not be profaned.
Didache 14 [A.D. 70]
Didascalia (Apostolorum), composed A.D. c.230, is a Christian treatise which belongs to the genre of the Church Orders. It presents itself as being written by the Twelve Apostles at the time of the Council of Jerusalem, however, scholars agree that it was actually a composition of the 3rd century, perhaps around A.D. 230, it was clearly modeled on the earlier Didache.
The apostles further appointed; On the first day of the week let there be service, and the reading of the holy scriptures, and the oblation [sacrifice of the Mass], because on the first day of the week [Sunday] our Lord rose from the place of the dead, and on the first day of the week he arose upon the world, and on the first day of the week he ascended up to Heaven, and on the first day of the week he will appear at last with the angels of Heaven.
Didascalia 2 [A.D. 225]
Eusebius of Cæsarea, (A.D. c.263-338), appointed Bishop of Cæsarea in A.D. 314, Roman historian, exegete and Christian polemicist, scholar of the Biblical canon who was deeply embroiled in the Arian controversy.
They [the early saints of the Old Testament] did not care about circumcision of the body, neither do we [Christians]. They did not care about observing Sabbaths, nor do we. They did not avoid certain kinds of food, neither did they regard the other distinctions which Moses first delivered to their posterity to be observed as symbols; nor do Christians of the present day do such things.
Church History 1:4:8 [A.D. 325]
[T]he day of his [Christ's] light . . . was the day of his resurrection from the dead, which they say, as being the one and only truly holy day and the Lord's day, is better than any number of days as we ordinarily understand them, and better than the days set apart by the Mosaic Law for feasts, new moons, and Sabbaths, which the Apostle [Paul] teaches are the shadow of days and not days in reality.
Proof of the Gospel 4:16:186 [A.D. 319]
St. Victorinus, (A.D. 260-303), an ecclesiastical writer who flourished about A.D. 270, and who suffered martyrdom probably in A.D. 303, under Diocletian.
The sixth day [Friday] is called parasceve, that is to say, the preparation of the kingdom. . . . On this day also, on account of the passion of the Lord Jesus Christ, we make either a station to God or a fast. On the seventh day he rested from all his works, and blessed it, and sanctified it. On the former day we are accustomed to fast rigorously, that on the Lord's Day we may go forth to our bread with giving of thanks. Let the parasceve become a rigorous fast, lest we should appear to observe any Sabbath with the Jews . . . which Sabbath he [Christ] in his body abolished.
The Creation of the World [A.D. 300]
The Apostolic Constitutions (or Constitutions of the Holy Apostles), dated A.D.c 270, is a Christian collection of eight treatises which belongs to genre of the Church Orders.
And on the day of our Lord's resurrection, which is the Lord's Day, meet more diligently, sending praise to God that made the universe by Jesus, and sent him to us, and condescended to let him suffer, and raised him from the dead. Otherwise what apology will he make to God who does not assemble on that day . . . in which is performed the reading of the prophets, the preaching of the gospel, the oblation of the sacrifice, the gift of the holy food.
Apostolic Constitutions 2:7:60 [A.D. 400]
St. Athanasius of Alexandria, (A.D. 296-372), Egyptian; bishop, theologian, and Doctor of the Church. He was present, as an assistant to St. Alexander of Alexandria, at the council of Nicea who he succeeded in A.D. 326. During more than forty years he was the champion of orthodoxy, and suffered much severe persecution from the Arian party.
The Sabbath was the end of the first creation, the Lord's day was the beginning of the second, in which he renewed and restored the old in the same way as he prescribed that they should formerly observe the Sabbath as a memorial of the end of the first things, so we honor the Lord's day as being the memorial of the new creation.
On Sabbath and Circumcision 3 [A.D. 345]
St. Cyril of Jerusalem, (A.D. 315-386), Palestinian; ordained by Maximus, he was made bishop of Jerusalem in A.D. 345; scholar and Doctor of the Church. None of his writings have been preserved to us, except eighteen catechetical instructions addressed to catechumens, and five mystagogic discourses addressed to neophytes.
Fall not away either into the sect of the Samaritans or into Judaism, for Jesus Christ has ransomed you. Stand aloof from all observance of Sabbaths and from calling indifferent meats common or unclean.
Catechetical Lectures 4:37 [A.D. 350]
St. Jerome, (A.D. 342-420), Dalmatian; born in Strido; priest, hermit, abbot, biblical scholar, translator and Doctor of the Church. In an age distinguished by men of the greatest eloquence and learning, St. Jerome, especially in all matters connected with the Sacred Scriptures, was then preeminent, and has probably never since been equalled.
The Lord's day, the day of Resurrection, the day of Christians, is our day. It is called the Lord's day because on it the Lord rose victorious to the Father. If pagans call it the "day of the sun," we willingly agree, for today the light of the world is raised, today is revealed the sun of justice with healing in his rays.
St. Jerome, Pasch.
St. John Chrysostom, (A.D. 344 - 407), Syrian; archbishop, Doctor of the Church. Born at Antioch in 344; he was ordained priest in A.D. 383, and raised to the see of Constantinople in the year A.D. 398. His eloquence gained him the title of Chrysostom, or the mouth of gold. His expositions of Scripture, especially the Epistles of St. Paul, are very valuable. This illustrious prelate died on his road to exile, in A.D. 407.
When he said, "You shall not kill" . . . he did not add "because murder is a wicked thing." The reason was that conscience had taught this beforehand, and he speaks thus, as to those who know and understand the point. Wherefore when he speaks to us of another commandment, not known to us by the dictate of conscience, he not only prohibits, but adds the reason. When, for instance, he gave commandment concerning the Sabbath —
"On the seventh day you shall do no work"— he subjoined also the reason for this cessation. What was this? "Because on the seventh day God rested from all his works which he had begun to make" [Ex. 20:10]. And again: "Because you were a servant in the land of Egypt" [Deuteronomy 21:18]. For what purpose then, I ask, did he add a reason respecting the Sabbath, but did no such thing in regard to murder? Because this commandment was not one of the leading ones. It was not one of those which were accurately defined of our conscience, but a kind of partial and temporary one, and for this reason it was abolished afterward. But those which are necessary and uphold our life are the following: '"You shall not kill... You shall not commit adultery... You shall not steal." On this account he adds no reason in this case, nor enters into any instruction on the matter, but is content with the bare prohibition.
Homilies on the Statues 12:9 [A.D. 387]
You have put on Christ, you have become a member of the Lord and been enrolled in the heavenly city, and you still grovel in the Law [of Moses]? How is it possible for you to obtain the kingdom? Listen to Paul's words, that the observance of the Law overthrows the gospel, and learn, if you will, how this comes to pass, and tremble, and shun this pitfall. Why do you keep the Sabbath and fast with the Jews?
Homilies on Galatians 2:17 [A.D. 395]
The Byzantine Liturgy, (prior A.D. 379)
The day of Christ's Resurrection is both the first day of the week, the memorial of the first day of creation, and the "eighth day," on which Christ after his "rest" on the great sabbath inaugurates the "day that the Lord has made," the "day that knows no evening."
Byzantine liturgy — CCC 1166