Joel is calling upon the priests to take the initiative in a general act of humbling themselves before the LORD. They are to lead the way by putting on sackcloth (i.e. with the garment of mourning) and also by making gestures of grief in other ways, obviously as a sign of sadness and humiliation and in this way appeal to God’s mercy. They are also to spend the night in sackcloth, which intensifies their expression of sorrow (See 1 Kings 21:27).1
By outward demonstration of your sorrow, you strengthen the inward sorrow that is at issue: the sorrow in your heart.
13 Put on sackcloth and lament, O priests; wail, O ministers of the altar. Go in, pass the night in sackcloth, O ministers of my God! Because grain offering and drink offering are withheld from the house of your God.