The term 'owned' or more commonly 'pwned' is a internet geek term that refers to 'ownage' by one player or person of another. Put more simply, during multi-player video games it was used to describe not simply beating a player, but destroying the other player in an overtly embarassing way. The term has grown over into other areas, sometimes real life. Most notably popular and funny in this context is it's usage in videos or graphics. Regular or familiar images have the term "OWNED" splashed across them.
Did you learn your lesson, little boy?
Here is my favorite example, an animated .GIF image of a little toddler on America's Funniest Videos. The kid was probably playing a little too close to the cat and the cat (thankfully declawed I think) got tired of it.
Would you like to learn more about pwnage? Be sure to check out some of the following resources (warning, though, some of them are not suitable for mixed company).