Every time we sin, we hurt ourselves, other people and God. The Sacrament of Reconciliation (also called Penance or Confession) was given to us by Christ to help us reconcile with Christ and his Church when we have committed harm. Through the Sacrament, we acknowledge our sins, express our sorrow in a meaningful way, receive the forgiveness of Christ and his Church, make reparation for what we have done and resolve to do better in the future. During his public life, Jesus both forgave sins and reintegrated sinners into the community. This is the goal of the Sacrament of Confession: to forgive sins and to provide reconciliation with the Church. The Sacrament of Penance & Reconciliation involves four parts: contrition, confession, penance and absolution.
Any of these is fine. The liturgical rite is officially called the Rite of Penance & Reconciliation. The Catechism of the Catholic Church notes the Sacrament is known by many names: