God’s wrath (see also Psalm 88:7) is released on the author and he feels overwhelmed. The Lord’s terrors threaten to utterly destroy him. Jesus will have recognized himself in Gethsemane in these words. In Luke 22:44 we read: And being in agony he prayed more earnestly; and his sweat became like great drops of blood falling down to the ground.
There he had to drink the cup of God’s wrath. That was the will of the Father and Jesus submitted himself to that. But oh, the cost was tremendous. God’s wrath pressed upon him extremely heavy, and all that because of our sins.
16 Your wrath has swept over me; your dreadful assaults destroy me.