Pax Domini is Latin for the Peace of the Lord. The Sacrament of Jesus’ body and blood is how the peace that the Lord gives, the peace that surpasses all understanding, true peace is given. Showing them His wounds, our risen Lord declared His peace to His disciples. That same peace of the Lord is given to us and all Christians in His body and blood.
The Pax was originally inserted into the liturgy at the end of the Service of the Word, but to better demonstrate the truth of the Fifth Petition of the Lord’s Prayer (forgive us our trespasses as we forgive those who trespass against us) it was moved after the Lord’s Prayer and before Communion, that is, after we pray for peace and immediately before we receive it. (John 14:27, 20:19 & 21)