One, it is a bit easier. You don't have to do all the establishment, you don't have to develop a world, and there is a fair audience.
Two, it is just fun. You get to goof around in a setting, doing things the original probably would never dare with the setting.
Three, it is decent practice to going to something all your own. Because you have a ready audience you can see what sort of things work and what don't. You can experiment with different, and different approaches and get at least some feedback. Go with something completely new and it will likely completely unnoticed.
Now those are the reasons I do it, but here is a few others too:
Four, it can get you a significant following. Again ready made audience, you catch their interest you can have quite the following going and that can stroke anyone's ego.
Five, you want to preach the good word... but do it subtly... or at least have deluded yourself into thinking your being subtle. Yes, a lot of authors will do this. Rather than argue on a forum about the series in question, they'll put their argument into semi-solid form in the way of a story.
Six, just to vent. Latest episode ticked you off? That particular character's fandom a bunch of no nothing losers? Well, time to break out the poison pen... er, keyboard, and tell them off by way of destroying them in story form.
As to why read it, mostly out of fun and lack of satisfaction with the available canon content.
That said, yes, a great deal of fanfiction is total and complete *bleep*. Hell, I've written some complete and total *bleep*, not the so *bleep* it is good either type. Nope, just plain *bleep*.