….when they say, “And with your spirit,” the people are addressing the “spirit” of the priest; that is, the deepest interior part of his being where he has been ordained precisely to lead the people in this sacred action. They are saying in effect, “Be priest for us now,” aware that there is only one priest, Christ himself, and that his one who represents him now must be finely tuned to perform his sacred duties well. If the priest’s greeting is like a blessing on the people, the people bless their priest in return. The people know that if their priest is “in this prayer” with all his heart, all his mind, all his soul, this will be to their advantage also, for at every point in the prayer he is their leader, and they cannot advance in it without him.
Father Jeremy Driscoll, OSB from his book What Happens at Mass.