Catholics offer a “sign of peace” to each other just before celebrating the Eucharist (at least in the Western rite) and the reason is pretty straight forward, Matthew 5:23-24 says
“Therefore, if you bring your gift to the altar, and there recall that your brother has anything against you, leave your gift there at the altar, go first and be reconciled with your brother, and then come and offer your gift. “
The basic idea is to be at peace with your “brother” when approaching the altar and it’s a continuation of the idea that we should be sinless (well, technically “in a state of grace”) when receiving the Eucharist and also that Communion is all about unity; and if we’re not united then we shouldn’t pretend to be.
The reason I bring it us is I had a chance to really experience this recently. My wife and two daughters and I were vacationing and—without getting into details—we were starting to get on each other’s nerves a little bit. We went to church fifty minutes early only to discover that that the directory had the wrong Mass time so we were actually ten minutes late. We slipped into the second-to-last pew as the psalm was finishing.
Approximately three and a half seconds later my oldest daughter had to go to the bathroom. One thing led to another and we had a pretty ugly conversation after we left the sanctuary. I was at my limit and let my frustration out to play.
Call it a Eucharistic miracle or whatever you’d like but as Mass continued I became more and more aware of the un-peacefulness in me and the passage from Matthew kept going through my mind. The sign of peace was spent hugging my daughter and apologizing to her. It was a great experience of unity with her and made me extremely grateful for the opportunity to make peace with her before receiving Communion.
My hope is that this helps me see the sign of peace as something more than an act where I smile and shake the hands of strangers around me and see it as an opportunity to come to the table of the Lord ready to receive him. God is good.