3 Then the Deacon cries aloud, “Receive ye one another; and let us kiss one another.” Think not that this kiss is of the same character with those given in public by common friends. It is not such: but this kiss blends souls one with another, and courts entire forgiveness for them. The kiss therefore is the sign that our souls are mingled together, and banish all remembrance of wrongs. For this cause Christ said, If you are offering your gift at the altar, and there rememberest that your brother has anything against time, leave there your gift upon the altar, and go your way; first be reconciled to your brother, and then come and offer your gift. The kiss therefore is reconciliation, and for this reason holy: as the blessed Paul somewhere cried, saying, Greet ye one another with a holy kiss; and Peter, with a kiss of charity.
Source: Catechetical Lectures (New Advent)