Comes from a Chappelle's show sketch where charlie murphy (eddie murphy's brother) is telling stories from the 80's when he used to hang out with famous people on account of his brother. they call it charlie murphy's true hollywood stories or something. and he's talking about Rick James coming over, all high on cocaine, with muddy boots, and kicking them all over Eddie's brand new expensive couch, and he's just yelling "FUCK YO COUCH, NIGGAH!" so they beat the crap out of him.
This phrase originated from, was popularized in, and was entered into prominence by Chappelle's Show in episode #204 where Rick James says "fuck yo' couch, nigga" when he is caught kicking mud all over Charlie Murphy's white couch.
The phrase entered pop culture lexicon to mean audacious indifference or apathy in acts of disobedience or to a given situation.