|Besides being an adjective meaning covered in fine hair,
"Furry" has a number of additional uses as a noun:
A furry is an anthropomorphic animal, that is an animal having some of the characteristics of a human like being able to walk on two legs, speak human languages, use tools etc. Many cartoon characters are furries: Mickey Mouse, Bugs Bunny, and they make frequent appearances in childrens literature such as the works of Beatrix Potter. They are not just a recent phenomenon either: furries also appear in Shakespeare and Aesops fables, and in darker works like Dr. Moreau, Animal farm, and every werewolf novel written.
Fans of furry art & literature often refer to themselves as furries too. Online they typically assume furry identites, and have furry characters on roleplaying systems like MUDs/MUCKs. For some of these furries there is a deeper connection that goes beyond appreciation of artwork and stories. This can include concepts such as totemism and spritual theriantropy. Whatever fuels their fascination with these animal-human hybrids, furries often have social gatherings - sharing stories, ideas, and art and generally having fun. If you see people with the occasional tail, animal ears, or full "fursuit" they may be furries.