Today is Ash Wednesday, the first day of the season of Lent. About ten years ago, a young adult friend of mine -- a cradle Catholic -- said on Ash Wednesday, "Nobody ever explained to me why we give up things for Lent." Ever since, I have wanted to write this, but being a procrastinator, it took me a decade. This is for Catholics who missed that part in their formation, as well as non-Catholics who are curious.
We practice penance to remit the temporal punishment due to sin. Although Christ's sacrifice was complete and thus opened the gates of Heaven to us, his sheep often cling to sin. We know that nothing can enter the Kingdom of Heaven unless it is perfect as the Heavenly Father is perfect (Mt 5:48). The remission of temporal punishment sanctifies the attachment to sin that we cling to, which would otherwise keep us from being perfect (CCC 1863). Penance and prayer (before death) and Purgatory (after death) are the ways Catholics believe this punishment can be remitted. We may also offer our penance for the sake of other people's temporal punishment, such as when we pray for the souls in Purgatory (CCC 1032).
If you are not Catholic, you don't have to believe in temporal punishment or Purgatory to make sacrifices during Lent. There are at least three more good reasons for Christians to do so, each less selfish than the one before:
To break our attachments to the world. Christ said that to enter the Kingdom of Heaven, we should give up not only all our possessions, but even our families (Lk 18:22-30). Although he was using hyperbole, his point remains clear: you cannot be attached to God if you are attached to the things of this world (Lk 16:13).
To unite ourselves to Christ's sacrifice, and to thus become more Christ-like. The nature of love is such that the lover becomes like the beloved. God, the lover of us, became like us, in fact became one of us. We, if we are lovers of God, naturally want to become like Christ.
Out of pure love. Our sacrifice is a gift to Christ. The nature of love is also such that it requires sacrifice when creatures (i.e. anything except God) is involved. This is why women suffer to bear children, why men vow celibacy to become priests, why both sexes give up things they want for the good of their families. In giving up our pleasures and replacing them with suffering, it is as if we are offering that pleasure to Christ instead of indulging in it ourselves.
Any errors in the above are due to my own misunderstanding, not to any rejection of, nor error in, Catholic teaching. Bible verses are meant as illustrations rather than as proof texts.