This kiss is different, affecting as it does a co-mingling of souls and mutually pledging unreserved forgiveness. The kiss then is a sign of a true union of hearts, banishing every grudge. So the reason you do it during the communion service is to demonstrate to your brother or sister that you are at peace with them, that you have nothing you are holding against them.
And he says, it was this that Christ had in view when he said, if when you are bringing your gift to the altar, you suddenly remember that your brother has a grievance against you, leave your offering by the altar, first go and make peace with your brother, and then come back and offer your gift. Join us in earnestly contending for the faith that was once for all delivered to the saints.