A fanlisting is simply an online listing of fans of a subject, such as a TV show, actor, or musician, that is created by an individual and open, and free, for fans from around the world to join. They are just a place where you can have your name listed along with other fans of the same subject.
Appropriate Behaviour is the fanlisting for the relationship between Worf (played by Michael Dorn) and Deanna Troi (played by Marina Sirtis) from Star Trek.
The name of the fanlisting comes from the season 7 episode, Parallels. There's a funny scene in that episode when Worf, who doesn't realise he's jumped into a Parallel Universe where he's married to Deanna, tells her I do not believe this is appropriate behaviour when she's trying to give him a backrub.