Most predominantly used in the greater New York area, "mad" is an appropriate replacement for Northern California's "hella" and Boston's "wicked." In the common vernacular, it translates into "a lot" or "extremely." Can be used almost interchangeably with any of the above listed words.

For the most part, it means angry.

When some little bitchboy is acting like a little tiny pee pee poo poo baby and messing up the group plans.

MAD is an American humour magazine with comics. The name should always be capitalized as "MAD" to distinguish with any other Mads or the word (adjective) "mad". MAD is an acronym from "Mesh takes a D", in which "mesh" is "#" (number sign) and "to take a d" is to "commit a suicide".

My brother is mad. He is mad that his definitions on urban dictionary got rejected.
I'm writing this to piss him off.

An international treasure. An Adidas-clad daddy with alpine cheekbones. Good at everything. Exceptionally gracious and charming. Men and women fall for Mads irrespective of sexual orientation.

Wikipedia says:
A MAD Movie is a Japanese fan-made video, much like an anime music video (AMV), that generally originate from the Japanese website Nico Nico Douga. MAD can also describe the Japanese AMV community, although they can be anything from audio clips, edited pictures, to wholly original creations. MADs do not necessarily even need to be related to anime, though the more popular ones typically are. The term MAD (occasionally M@D) is thought to be a reference to the name of one of the original MADs, rather than a particular acronym for anything.

1: really or extremely
2: alot