Joss's work is not unlike South Park in being a juxtaposition of conveying subtle and sophisticated points through a juvenile medium. Where South Park is complex social commentary amid toilet humor, Joss almost invariably demonstrates in an exaggerated yet realistic way the subtleties of human behavior and social interaction, against a fantastical and over-the-top backdrop. This study of culture, roles, and behavior is not unlike The Office, but instead of being in a setting we are all familiar with, it happens among monsters and heroes.
Another element that makes Joss Whedon's work so distinct is his tendancy to identify a common genre convention, then play with viewer expecation by turning it on its head. I think this is part of the reason he is so fond of killing off main characters. It defies our expectation that characters that we love are somehow protected by our fondness, and by making the world less safe it also makes it feel less artificial.
A more silly example of this device is the the opening scene of Dr. Horrible, (itty bitty spoiler alert,) opening with the dramatic maniacal laugh, but then transitioning to a down-to-earth monologue. I can think of a dozen tiny moments like this in his other work. In Buffy, the dramatic evil villain speech that gets unceremoniously cut off; in Firefly, Mal insisting that no, really, he doesn't need to do this for himself -- please give him a hand; a million subtle changes in pacing that surprise you, though you don't quite know why.
Then of course there is the witty dialogue, hot babes, and cool shit. Yes, yes I am a fangirl.