Theoretically a push up done in a handstand. In actuality, a push up merely done without wearing underwear. So, when a guy is bragging that he can do commando push ups, it may not be what you expect...
Guy: Guess what? I did 12 commando push ups last night.
Girl: Really? What's that?
Different Guy: Oh, shut up, dude. It just means he did push up 'au naturale'.