It’s frowned upon, I know, which I think is a real shame. Some of that stuff is amazing. I’m not linking to my own as it was started when I was 14 and has been halfway through book 3 for over 10 years but there’s some other great material. I had to Google it but apparently it was T.S Eliot who said “good writers borrow, great writers steal.”
And that’s sort of where fan fiction is. Mine are Harry Potter related but they’re far from the only ones, with thousands of others for Narnia, Middle Earth, Panem, Twilight and others – indeed the 50 Shades series began as Twilight fan fiction. I’ve not read either series so can’t really say how much remains of the original or how good either is, but that’s not the point.
The point is they’re a springboard. Unsure of your own story? Start with someone else’s! I know that ideas, characters and plot lines that I invented during my Harry Potter days directly influenced other writing down the line. They may not get used, of course, but they started the thought process.
If nothing else, it’s a lot of fun and some school teachers seem to like it; I got very good marks for the River God (Wilbur Smith) short story written back at secondary school…