An exclamation of celebration, usually used when articulating positive feelings towards news that was just received. Conveys the enthusiasm beyond that of simply "awesome" by emphasizing what is not only a capital letter, but one which doesn't belong in the word at all.
The spelling (but not the pronunciation) of this word was made famous on www.homestarrunner.com (H*R) by the "aweXome cross '98" event, and subsequent video game.
Person 1: "Did you hear that they're making that into a movie?"
Person 2: "Seriously? That's aweXome!"