80:1 Cherubim are mighty angels. That God “dwellest between the cherubims” is a reminder of his presence on the Ark of the Covenant (Exodus 25:17-22).
80:3, 7, 19 Three times the writer calls on God to “turn us again.” Before God can turn us to himself, we must turn away from sin. Repentance involves humbling ourselves and turning to God to receive his forgiveness. As we turn to God, he helps us see ourselves, including our sin, more clearly. Then, as we see our sin, we must repeat the process of repentance. Only then can we constantly be restored to fellowship with God.
80:17 The “son of man” is probably not the Messiah but Israel, whom God calls elsewhere his “firstborn” (Exodus 4:22). The psalm writer is making a plea that God would restore his mercy to Israel, the people he chose to bring his message into the world.