It means you were made to look like the inferior Internet-Junkie that you are. Of course, if someone corrects someone's grammar, to some folks that's justification for an "OWNED" picture.
I believe the term originated from Counter-Strike. There, it refers to when someone repeatedly gets killed and loses. Of course, it also applies to other games and situations. Thus, the owned pic was created.
For example, the German guy in my sig might be referred to as being owned.
Hmm, well if i saw an owend picture i'd be pussled. WTF is OWEND?
OWNED on the other hand is a different story. Some people like to put the word across pictures of people failing, suffering or all around mysery. It makes them feel better about themself and provides a laugh.