In truth, just someone who's into the concept of anthropomorphic animals and/or self-identifies as such. The criteria so to speak on what makes you a furry is to say the least, very subjective in my opinion. To me, its when you identify as a furry that you're part of the community after discovery.
There are differnet levels of anthropomorphism too. From a feral animal that can talk, to a full blown humaniod body shape with fur, a tail, animal head, etc.
See the misconception is everyone thinks that being a furry means you dress up like animals and have sex with other people who do or actual animals. No one (or very few) people actually do that. Furry's are just people who like the design of humanoid animals like Star Fox or others. In that sense I'm kinda a furry