In a movie I watched there was a scene where there was a couch delivered to a house. The owner of the house is telling some workers where to place it. She says "We were thinking in here" while pointing to a room which they were entering and after they are inside she points to a wall and says "with the coming-out part along the wall". The couch is basically a corner settee but two-piece not one, with a little table in-between. What is the coming-out part of a couch?
It means “the part that comes out”. The descriptive clause (“that comes out”) has been transformed into an adjective phrase (“coming-out”). Some similar constructions are:
The rubbed-out part said something interesting. (There is a part of the writing that was rubbed out.)
The combed-over part doesn’t hide much. (There is a part of their hair that is combed over the top of their head.)
The tidied-up part looks as good as new. (There is a part of the area that has been tidied up.)
Exactly what part of the couch this is must depend on context. It likely means one side of the corner piece—the speaker considers one side (the longer one?) to be the “main” one, and in their mind, the other side “comes out” from there. They want that other side to lie along the wall.
It could equally mean other things for different furniture. A sofa bed has a part that “comes out” in the sense of folding out when needed. I personally might use “comes out” to describe the part of a corner piece that does not follow the wall (it “comes out” towards the middle of the room), but that’s clearly not the case here!