Out of the realm of what is considered normal - almost to the extreme. Can be used to express an excessive amount of another word - both adjective, verb and noun. Obscene awesomeness. Obscene waterskiing. Obscene hairdo.
Expression as to whether this is a good thing or bad thing is taken in the context.
Dude, did you see the booty on that chick - it was obscene (in this case, defines as big).
The obscene awesomeness of this party is wreaking havoc with my brain.