Writing is a fairly intimate exercise and lets you explore ways in how you can express yourself. It can also be an educational experience in that it will reinforce proper usage of grammar and spelling, you can acquire a sophisticated diction, and learn how to describe things in a coherent yet creative way.
But above all, especially when you are writing fan fiction, just have fun with it! Don't take it too seriously. Remember, this is not an integral part of your life and at the end of the day, it's only a story.