It also means to snap your hand back to your defensive position. Don't leave it hanging out there cuz you'll get smacked in the head. After a punch, always bring your hands and arms up to your guard to protect your head and body.
So I think your instructor's implying that you should snap your punch out and then snap it back. It sounds simple, but after a while it gets exhausting. With practice, it becomes second nature and you won't think about it.