A fanlisting is simply an online list of fans of a subject (in this case for amber) that is created by an individual and open for fans from around the world to join.
There are no costs, and the only requirements to join a fanlisting are your name and country. Fanlistings do not have to be large sites (although some are), they are just a place where you can sign up with other fans. TheFanlistings.org is the original (but not official) web directory for fanlistings, dedicated to uniting the fans.
Description from tfl.

amber

the mysterious one

A mysterious girl related to Hell's Gate, disappeared with Bai five years prior to the story in South America. She was in the same organization as Hei back then, but originally a spy for MI6 with the codename February. She is the one who holds the meteor fragment. Amber's ability is to freeze time, though her remuneration has not been shown yet. However, it has been noted as something she can do a finite number of times.She is currently looking for something called the "key". It seems to be she cares quite greatly for Hei. Source:wiki.