Dat ass is a meme originating from 4chan of all places (who woulda guessed). It started as one anon's desperate request for an ass thread which was shortly followed by another poster using a picture of the rapper Rich Boy biting his lower lip with the words "Dat ass" slapped on the bottom.
A meme is essentially an idea in one form or another. More recent the word has come to represent fads on the web which has gained enough popularity to officially wear the title of meme. For more information on theory of the meme one can always look towards Richard Dawkins in The Selfish Gene, where the idea originated.
As with most memes it has spun off multiple instances since its introduction in 2007. Mostly with different people making strange faces with the words "Dat ass" within the image. There are also many instances using words with or similar to the word ass, with an accompanying picture. i.e A picture of the periodic table of elements with the words Dat mass shopped in.