G.W. North emphasizes the significance of the priestly offering in his sermon, explaining that the Old Testament sacrifices were merely shadows of the true offering that Jesus made. He highlights that true worship involves a life of offering oneself to God, free from the burdens of sin and guilt, and that believers are called to live as priests, offering spiritual sacrifices that are pleasing to God. North encourages the congregation to understand the importance of their priesthood and the need for genuine offerings that come from a heart of compassion and obedience to God's will.