An ascetic form of penance is to act penitent or remorseful and punish oneself (see Colossians 2:18-23). Another form of penance is trying to do enough good deeds to outweigh and make up for one's sin. Both imply that we must pay for our own sins—but none of us could ever do enough to pay for even one sin.
All sins are evil because they violate the perfect, loving laws of our Creator God. The only sacrifice great enough to pay for the guilt of our sins has already been offered—the suffering and death of the Son of God, Jesus Christ. So doing penance is a gross insult to God. It implies that Jesus' sacrifice and God's grace are unnecessary.
And what is God's "grace"? It is the totality of all the gracious gifts that God offers to mankind. And among the greatest of those gifts is the complete forgiveness of all past sins. That, in turn, opens the door to all the rest of God's gifts, including the ultimate gift of eternal life (Romans 6:23). "For by grace are ye saved through faith; and that not of yourselves: it is the gift of God" (Ephesians 2:8, King James Version).
But don't confuse grace with its counterfeit—"cheap grace." Grace means forgiveness of past sins, not permission to continue sinning, as Satan would like for us to think. Jude warned of "godless men, who change [pervert] the grace of our God into a license for immorality" (Jude 4, NIV; compare Romans 6:1-2).
Grace is made possible by Christ's sacrifice and by Him serving as our merciful Mediator, Advocate and High Priest (1 Timothy 2:5; 1 John 2:1-2). "Seeing then that we have a great High Priest ... let us therefore come boldly to the throne of grace, that we may obtain mercy and find grace to help in time of need" (Hebrews 4:14-16).