I read something. Rather I like it or not, the writer part of my brain automatically wants to write about it. If I like the ideas, and I'm not ashamed to say I actually read that, I might translate that into fanfiction.
As a fanfiction writer, I see fan creations as a gateway to original works. Experimenting with fanfiction gives the writer experience with characterization, dialogue, sticking to previously established rules, grammar, formatting, title-giving, and summarizing. Fan art is a lot like this as well. Using fan art, the artist can learn about proportions, colors, facial expressions, and much more. Someone who can't draw can start with fan art, and slowly build up to the more original pieces, until they are doing their own work.