Sin harms our relationship with God and damages our communion with the Church. Conversion of heart is the beginning of our journey back to God. Liturgically this happens in the Sacrament of Penance. In the history of the Church, this Sacrament has been celebrated in different ways. Beneath the changes, there have always been two essentials: the acts of the penitent and the acts of Christ through the ministry of the Church. Both go hand in hand. Conversion must involve a change of heart as well as a change of actions. Neither is possible without God's grace.
(From USCCB Sacrament of Penance)
Since our sins are concrete acts that we've performed in the real world, with real harmful consequences to ourselves and to the larger world we are a part of, the act of atoning for our sins likewise needs to be performed as a concrete act. When we confess our sins, we experience more personally God's forgiveness; when we perform our penance, we help in some small part to repair the damage our sins have inflicted on the Church.