A published fanfiction is a story set in the same universe (or sometimes a parallel universe) with some or all of the same characters from the original story. Sometimes it shows the story from a different perspective, sometimes it shows the events before or after a series started/ended. They're not always what you expect, especially if there is a different author than the original series.
A few examples are
-Fifty Shades of Grey series was a fanfiction of sorts from the Twilight series
-the new "Cursed Child" play, which is a continuation (of sorts) of the Harry Potter series
What are some published fanfiction/spin-offs you like? Why do you like them? Are they very different from the original series? Have you ever read any books that came AFTER the movies? For example, the first Star Wars book was based off the script for the first Star Wars movie, though it was published before the movie actually came out.