A furry is any sort of half-animal/half-human creatures, usually bipedal. Most commonly appearing in the form of "talking animals" or "animal-headed people." Many are familiar cartoon characters, such as Bugs Bunny or Mickey Mouse.
A furry is also sometimes used as shorthand to mean a furry fan, i.e., anyone who likes anthropomorphic animals. There is a small but growing fandom
for people who like furries.
A furry hater
is someone who is willfully ignorant about furries
and goes around making stuff up about them on UrbanDictionary.
The common response from people when you ask "Have you ever heard of furry fandom?" is "No." That doesn't mean they're furry haters, they've just never heard of furry fandom.
Furry fandom is pretty awesome.