What does the sofa gag mean?

In short, each episode has a different joke/scene/story related to the sofa of The Simpsons.

Look at the English explanation:

Couch gag is a continuous visual joke at the beginning of the animated TV series The Simpsons. Couch gag changes from one episode to another, usually featuring the Simpsons' living room sofa. A typical joke is that the Simpsons ran into the living room, only to find that there was something wrong with the sofa. Whether it's a strange and unexpected occupant, a strange sofa location, such as the ceiling, or any other situation.