Before I answer your question, I think it would be helpful to explain what the “penitential rite” is.
The penitential rite is a part of the Introductory Rites of the Mass that come before the Liturgy of the Word (when we hear the various readings from the Bible). It begins with an introduction by the priest, followed by an act of confession and penance by the people, and concluded by words of general absolution by the priest. The penitential rite, like the Eucharist, effects the forgiveness of venial sins, but mortal sins must still be forgiven through the Sacrament of Confession.
Now, there are different options for the priest and the people during this rite. For our part, we usually say the Confiteor (“I confess to Almighty God and to you my brothers and sisters …”) or the “Lord have mercy, Christ have mercy, Lord have mercy” in response to the priest. The act of penance, at least when the Confiteor is said, is the striking of the breast three times.
Why do we do all this? The purpose of the penitential rite is to prepare us to celebrate the Mass by compelling us to call to mind our sins and by healing the wounds that divide us as a Body and weaken our relationship with the Lord. Then, with pure hearts and fully united, we can receive the Lord through the Word and the Eucharist.
This act of confession, penance, and absolution that takes place in the Mass is deeply rooted in Scripture and Tradition. John tells us in his first letter, “If we confess our sins [to the Lord], he is faithful and just, and will forgive our sins and cleanse us from all unrighteousness” (1:9). James tells us to also confess our sins to one another: “Therefore, confess your sins to one another, and pray for one another, that you may be healed” (5:16). These two verses together become the Scriptural foundation for the beginning of the Confiteor, when we say, “I confess to Almighty God and to you my brothers and sisters that I have sinned …” For his part, St. Paul says, “Let a man examine himself, and so eat of the bread and drink of the cup” (1 Cor 11:28). You could say that the penitential rite is our way of taking him seriously.
A penitential rite in some form has existed in the Eucharistic liturgy from the earliest days of the Church. For example, a Christian text from the 2nd century called The Didache (or “Teaching of the Apostles”) gives us these interesting instructions: “Assemble on the Lord’s Day, and break bread and offer the Eucharist; but first make confession of your faults, so that your sacrifice may be a pure one.”
And so we continue to seek communion with the Lord and one another in the Mass until that day when Jesus comes again and unites all things unto Himself.