Fr. Jan Larson, a priest of the Archdiocese of Seattle, has posted a thoughtful essay about the Sign of Peace on his blog, Liturgy Reflections. Here is an excerpt:
The greeting of peace is still a part of our liturgical prayer, really a kind of blessing that we exchange with those nearby, and this attitude of prayer and blessing ought not to take second place to other praiseworthy impulses. Thus care must be taken that the sign of peace does not become a sort of “time out” from the liturgy so that people can chat and socialize. That the sign of peace reflects a certain composure and restraint also applies to everyone else in the liturgical assembly. The church’s norms describe the sign of peace as the rite “by which the Church asks for peace and unity for herself and for the whole human family, and the faithful express to each other their ecclesial communion and mutual charity before communicating in the Sacrament…”
You can read the whole thing here.