Learn English – How did the slang meaning of “owned” come to be

Believe it or not, Wikipedia actually has an entire article dedicated to the word.

Owned is a slang word (e.g. "Wikipedia got owned!"), that originated among 1990s hackers, where it referred to "rooting" or gaining administrative control over someone else's computer.

The term's original usage was close to that of the traditional meaning of the word "own" — for instance, "I owned the network at MIT" indicated that the speaker had cracked the servers and had the same root-level privileges that the legitimate owner of the servers had. "Owned", a later variant, became more common in the late 1990s, as did the more abstract usage referring to any compromised security mechanism. By 1997, "owned" was regularly used in website defacements, and it subsequently spread to gaming circles, where it was used to refer to defeat in a game.