I've been assigned an essay on "The Overcoat" which asks the following question:Explain how the metaphor of copying successfully advances Nikolai Gogol's purpose in "The Overcoat." I do not understand where the metaphor of copying lies in the story beyond his job involving copying.

A central theme or purpose of Gogol's short story is to expose people's lack of compassion. He also shows that acts of inhumanity are copied by others.
People do not "see" Akaky beyond his outward appearance as a lowly copying clerk who wears an old coat. He is treated rudely by his superiors and his coworkers because of how he appears on the outside: low status and poorly dressed with imperfect social skills. Nobody truly understands him in his inner humanity.
Akaky is a copy clerk, and he loves his job. He loves copying and derives satisfaction from doing his job well. You can find a number of quotes in the story referring to how much Akaky likes his job; Gogol emphasizes this because it is important.
Getting the new overcoat made, however, comes to rival copying in capturing Akaky's interest and attention. When he gets the new overcoat, he feels his self-esteem rise. If copying made Akaky feel good internally, the coat makes him feel like a new person on the outside. It also excites other people's interest and leads to the party being thrown for him.
When robbers steal Akaky's coat, two inhumanities occur: the first is the inhumanity of stealing a coat from someone in the middle of a Russian winter. The next is the way people go back to treating Akaky as lowly when he shows up in his old, tattered coat. If success (the "success" of gaining a new overcoat) breeds success, so does inhumanity breed inhumanity.
At the end of the story, after Akaky dies, people believe the ghost of this copy clerk is engaging in copycat crimes, namely, ripping overcoats off the shoulders of living people. Akaky's role as a copy clerk ultimately entails his role as a ghost copying misdeeds done to him. This seems to reflect people's haunting anxiety that those who have been treated with little compassion will come back to "copy" inhumane treatment.