How often have you watched a movie, read a book or watched a series and though :"I wonder what would happen if..." ?
A-ha. And then you've thought about this question and came up with several possible storylines, right? See, that is fanfiction! (If you have never made up stories like that, then go and do something for your imagination!)
You can write fanfiction about absolutly everything: more obvious things like movies, series and books, or less obvious ones like your favorite band or baseball team. ("What happened when the Rolling Stones met the New York Yankees") You just write about whatever you love. :-)
That is, by the way, the reason why fanfiction usually seems ununderstandable if you don't know the fandom. Fanfiction writers presume that their readers know the characters. If I write a Newsies story for example, I don't explain who Jack Kelly is, or what Sante Fe means to him. (If you don't know Newsies then you didn't understand this sentence - which proves my thesis to be true.)
If you've never written fanfiction, just go ahead and try it! It's a lot of fun, and it makes you feel very good to write the stories, that are in your head, down. If you feel shy about it, remember that you don't have to show your story to anyone if you're not happy with it.
I needed a while myself to gather the courage - I wasn't sure whether my English would be good enough. (I'm German by the way.) But when I finally started I had so much fun and now I can't stop anymore...I have lots of stories planned, and no end in sight...
If I can do it, so can you. Just go and have a try!