"Furry" when used as a noun seems to refer to one of two things:

     a) An animal-like character known as a "furry"
     b) A person who is a "furry fan"

 The latter is easy enough (knock on wood) to define:  A person who
 particularly enjoys stories, pictures, dolls, video games or whatever
 concerning "furry" creatures.  Defining a "furry" creature is somewhat
 harder, though.  There are several definitions depending upon which "camp"
 in furrydom, for lack of a better term, you might be in.

 The basic definition for a "furry" is an anthropomorphized animal
 character.  In other words, an animal character given human-like
 attributes, such as sapience and often a humanoid form.  The term "furry"
 is a misnomer, as a creature does not need to have fur to be "furry" in
 this sense.  Other terms sometimes interchangeable with a "furry" in this
 sense are "zoomorph", "morph", "anthropomorph" or (debatably) "funny
 animal".

 The core definition of a "furry" seems to include basically humanoid-formed
 creatures with animal faces, fur/scale/feathers/whatever, and often
 appropriate tails, wings, claws, etc., able to speak, and with a human-like
 personality, though quite often with "quirks" hinting at the real-life
 animal upon which the character is based.

 A broader definition will sometimes include other odd creatures that simply
 have some sort of animal features in their makeup.  Such would include
 mythical creatures such as centaurs, manticores, satyrs or harpies, all of
 which have human faces though more-or-less animal-like bodies.  This
 broader definition might also include the human-like characters that appear
 in some Japanese animation that have an animal tail and ears, but otherwise
 look about as human as any other anime character.

 One of the narrower definitions held by some is that in order for a
 character to be truly considered "furry", the character must exhibit
 animal-like characteristics in behavior.  Optionally, the fact that the
 character is an "animal" must be a major ingredient to the story.  This is
 exhibited in a frequent criticism of "furry" stories by those who hold this
 view: Many stories, while featuring characters fitting the core definition
 of "furry" given earlier are criticized as being "humans in animal suits"
 if their behavior isn't distinctly animal-like in some way.