What is happening here
The Communion Rite gathers everything that the Eucharistic Prayer has accomplished and makes it available to the assembly. It opens with the Lord's Prayer — the only prayer Jesus himself taught, prayed in this place at every Mass for fifteen centuries. Catholic tradition has always understood the petition "Give us this day our daily bread" as having a Eucharistic dimension; we ask for the bread of life that is about to be given.
The Sign of Peace follows. Some find this disruptive; others find it warmly important. Both responses miss what the rite is doing. Catholic theology holds that we cannot rightly receive the Body of Christ in the Eucharist without being in peace with the Body of Christ that is the Church. The Sign of Peace is not socializing; it is the assembly's sacramental gesture that they are reconciled with one another, ready to share the same Bread.
Then comes the Lamb of God ("Agnus Dei") — "Lamb of God, you take away the sins of the world, have mercy on us." This ancient litany prepares the assembly for Communion by addressing Christ as the Lamb whose sacrifice they are about to receive. The priest holds up the consecrated host and chalice, the assembly responds with the centurion's words from the Gospel — "Lord, I am not worthy that you should enter under my roof, but only say the word and my soul shall be healed."
Then the assembly approaches. The Communion procession is one of the most ancient rites of the Mass — the People of God walking forward, hands extended (or tongue extended), to receive the Body of Christ. Catholic teaching holds that this is the closest physical union with Christ available to us this side of heaven. The priest or extraordinary minister offers the consecrated host with the words "The Body of Christ"; the communicant responds "Amen." That single Amen is an act of faith in everything the Catholic Church teaches about the Real Presence.