The word "Furry" has more than one meaning in the Furry Fandom.

First off, a Furry is a person that associates themselves with the Furry Fandom. This is similar to how a fan of Star Trek might identify themselves as a Trekkie.

The word also means an anthropomorphic animal character like those found in Ashop's Fables, Disney's Robin Hood or the Secret of Nimh. Examples of Furry characters are literally everywhere, but are more common in children's media.

Often the word is used as an adjective to highlight that the noun following it has something to do with anthropomorphic animal characters. For example, the Secret of Nimh is a Furry Movie and Anthrocon is a Furry Convention.

The subculture is called the Furry Fandom because it's driven by and exists for fans of Furry characters.