Sometimes fan-fiction allows people to not have to go through character development and other difficult tasks, and simply play with an existing universe, which saves time and sometimes has marvellous results which can expand and increase the value of that universe. That's its highest achievement, and it's not very commonly seen.
Mostly though, fan-fiction is a way of avoiding real writing, with your own characters, and the risks and obstacles involved with that. It's a method of escape from copyright law, and from the shackles of fixed fictional worlds. With fan-fiction, you can make any two already-created characters, from any fictional universe you care to name, fall in love like you believe they were supposed to. Inevitably, this particular ability creates great works of ugliness when combined with teenage writers, the amateurs among them usually interested in about two things in the world - sex and romance, and neither of them are they particularly experienced enough to write about.
Most fan-fiction, I think it's fair to say, is not up to the standards of published writing. Like any publicly available information, it often lacks the refining influence of editors and the professional attention of critics. However, it gives freedoms that people didn't have before with written material. It allows for expression in old avenues, in new ways. Like with anything, between the best and worst you can see of it lies the average, and I think that more methods of expression are usually a good thing for personal liberty. Maybe writing a fan-fiction has saved a teenager's life, more than once. Or reading one. And that, I think, is laudable enough to pay the rest as interest.