The Guy on the Couch is a character appearing in the classic 1990s drug comedy Half Baked, portrayed by Steven Wright. He only appears in a few scenes, and is not that important for the plot, being basically a gag character.
The joke of "The Guy on the Couch" is that he has been sleeping on the couch of the four stoner roommates for several months, with no explanation of his origin or activities, and he only wakes up long enough to say a few words or, in one scene, use the bathroom. At one point, the roommates have an argument, blaming each other for "your friend sleeping on our couch", when they all realize that they had assumed he was a friend of one of the others.
The joke of "The Guy on the Couch", like many of the jokes about stoners in Half Baked is that it exaggerates something that all stoners have experienced, and while taking it to ridiculous extremes, it still seems familiar. The idea of a moocher who is only marginally known to someone hanging out in an apartment for an extended time is a familiar part of stoner life, even if the elements of him being constantly asleep, and totally unknown to anyone, are exaggerations.