Slang for male masturbation. The rigorous, reciprocating motion of your hand comprises the "punching," while the "dragon" is your penis. Presumably originated from the fact that ejaculation can rather resemble fire being breathed by a dragon, if you have sufficient technique, anatomical predisposition, and you eat enough BWW Wild sauce beforehand for color and sensation.
G-Money: "Whoa! That new waitress is hot. On an unrelated note, you boys will have to excuse me while I go to the restroom."
B-Ryan: "He's totally in there punching the dragon."