Telling someone to seriously fuck off. Don't just go suck a dick, but suck a fat dick. Especially if it's a weak or lame thing that the guy did.
-- Hey man, I took some money off your dresser. Then a bunch of dudes at the bar talked me into buying rounds. I'll pay you back though, as soon as I get my next paycheck.
When something really bad happens. Comes from suck and in this case it is sucking something big and fat. Used in the worst of situations when not much else can be said.
Doctor: I'm sorry, but you only have a few more months to live.
Man: Damn. That sucks a fat one.
Short-hand for the word floccinaucinihilipilification, meaning the estimation of something as valueless (encountered mainly as an example of one of the longest words in the English language).