The speaker admits, almost casually, that she's only involved with this man because of the people he knows. Her tone is flat and a little cold, as if she's not trying to hide her motives. But the poem quickly turns the joke back on her. The man tells her that those well-connected people are obsessed with other people, and that they spend their lives trying to impress each other. The word "people" repeats so often that it starts to sound empty, which is the point: fame here is a closed loop of folks worried about what other folks think.
The last three lines shift the mood. He writes about these people, lies in bed with them, and ends up "writing to me." That suggests he is still caught up in the same world he criticizes, and that the speaker is just one more person in the chain. The poem feels wry and detached on the surface, but underneath there's a hint of loneliness and irony.