This is my Ranma 1/2 Fanfic page. Let's start from the top.
Ranma 1/2 is a Japanese comic, both print and video, created by Romiko Takahashi. (Note that Japanese print comics are called manga while TV/Video comics are called anime). It is a romantic comedy about a boy who is cursed to change into a girl when splashed with cold water. It is/was very popular in Japan, and fairly popular in North America and other parts of the world.
(Note that this comic is complete, in the sense that the artist is not creating new episodes, and the entire series is available in many languages).
A fanfic is piece of fiction written based on the characters and settings in another artistic work. The name comes from the idea of fans of some work, producing fiction based on it. There's quite a bit of fanfiction floating around the internet. Check out fanfiction.net for a (large) sample.
And before you ask, no writing fiction based on other peoples copyrighted work is not illegal. At least not quite. As long as no infrigement is intended and there is no profit made from the work, you should be okay. Most artists are happy to see fanfiction based on their work, as it both indicates and stimulates interest.
I do other things besides write fanfiction. But those things are handled on other pages. I like to keep my hobbies and my work as separate as possible.