It's a two-way work sample. I see a sample of the writer's manuscript, and they see a sample of my editing work. Depending on several factors that I won't go into here, it may be a sample of developmental editing, of substantive editing, or of both.
What purposes does it serve?
It gives both the writer and me information we need to decide whether to enter into an editing relationship with one another. I guess that might sound a little strange, but here's what I mean: