What is an epilogue in a book? Why is it used?

The purpose of an epilogue is to help flesh out what happens after the story is done.

Have you ever read a good book and when you get to the end of the story, that's the last page? Do you ever sit there wondering - I wonder what happened to the main characters? I wonder how things worked out after the main story ended?

That's the purpose of an epilogue - to help flesh out what happens after the story is done.