From the Our Father at Mass, we are preparing for Holy Communion; first the priest’s Communion by which He completes the sacrifice, then the communion of the people who are united in the peace of Christ. This peace and unity is deeper than a political achievement, it is a state of fellowship in Christ and in the Church.
The various prayers at this time speak of the peace of Christ. First, we ask the Father to deliver us from evil and to grant peace in our days, so that helped by His mercy we may be free from sin and distress. We recall the peace given by Christ to the apostles and ask the Lord not to look on our sins but on the faith of the Church. The priest greets the people with the peace of the Lord, and we ask the Lamb of God to grant us peace.
There is a possibility for an external sign of peace, though the Church has made clear that this is optional, depending on circumstances and that it should not disturb the preparation for Holy Communion. The most important thing is that our peace comes from the altar, from Christ Himself, and that we should join ourselves sincerely with the prayer of the Church for deliverance and for the forgiveness of our sins.