A combination of two words, namely "what's" and "that".
A lazy, slang way to ask the question "What's that?"
Boy 1: "Hey did you hear about Daz and Sarah gettin' nakie in the club last week?"
Boy 2: "Wassat?"
Anatomist: "So I was studying the Hyopglossal nerve today and discovered it wasn't as close to the ansa cervicalis as I had previously thought."
Uneducated person: "Wassat?"
Pervert: "I bought a whiz bang sex machine with double pop rivets today."
Naive person: "Wassat?"