Sometimes the unitiated ask, "Why fanfic?" If you're going to write a story, they say, why not go full-out and create your own original characters and settings? Well, cuz we're lazy. And obsessive.
The first reason we write fanfic is because we love the fandom. Some imaginary world of another person's creation grabs us, drags us in, makes us wish it was real. We want to frolic in the false reality, own the gadgets, talk to the characters. Sadly, that isn't going to happen. So we go to the next best thing. We take control of our favorite characters, plop them into a situation of our own invention, and see what happens. We get to have fun with the character, and we put a little bit of ourselves into them and their world.
The second reason is the "what if?" obsession. Sure, we've got these nice characters, and the official creators make them do stuff. But we can't help wondering, "what if he hadn't...", or "what if she met a guy who...", or "what if they all were suddenly confronted by a purple monster who came to our galaxy to steal all our improperly programmed VCRs?" Since we can't all call up TV producers and demand to see our myriad fantasies on the screen, we write the story ourselves.
The third reason is very simple. We are lazy, and uninventive. Why go through all the trouble of inventing characters with personalities and back stories, worlds with strange conflicts and weird modes of transportation, *and* a plot? It's so much easier to steal the first two from a well-established series, and just worry about the third.
That's why we write fanfic. Maybe someday we'll get the guts to write a proper novel. Meanwhile, we'll practice our writing skills, develop our own style, cause much mayhem, and blatantly self-insert. All with a smile, and a disclaimer.