From Japanese doya-gao (ドヤ顔, どやがお). A smug face made after a win or something
epic (or not). Doya-gao, because of this nature, tend to be irritating.
This word started in Kansai stand-up comedians, and became
popular in the M-
1 Grand Prix 2006, a manzai tournament. It was adopted quickly on the
Internet, to the point where they had a whole TV program named with the word.
The Germans have a distinct word for it. It is "Backpfeifengesicht", which is a compound word that means "a face badly in need of a fist". Or a crowbar.
See also trollface, bitch slap, Umad? and Backpfeifengesicht.