Stories never really end...even if the books like to pretend they do. Stories always go on. They don't end on the last page, any more than they begin on the first page.

This quote means that the end of a book, or a story, does not really mean the end of the story. Even though the book might make it seem like the story resolves and has ended, the story actually continues beyond that point and doesn’t actually start at the beginning of the book either. It could be interpreted as saying that a story is an ongoing thing that continues beyond the existence of the book.