When Christians talk about self-denial they usually mean denial of things bad for us.
We acknowledge our sin-tainted nature and its disordered desires and attempt to discipline it according to the true and the good. By being virtuous we conquer our desires to do what is wrong as well as our desires to avoid what is right.
Secondly, at times Christians deny themselves even things that are good in themselves, for purposes of penance. For example, refraining from eating meat on Fridays is a traditional fast that helps us atone for sin and keep us strong for future battles. It is easy to become spiritually lazy and fall to sin without practices of penance.