A 'furry' from my experience is a person who has a love of anthropomorphic animals (usually animals made into a human form, like a werewolf - bipedal stance, maybe humanoid features, etc.) or animals in relation to humans. Their interest/love may come from a spiritual/totem-based background, a sexual fetish, or just an all around fascination, among all sorts of other reasons for their interest. Also, 'furries' may include people who have a specific spiritual connection to a particular animal. Usually the extreme 'furries' are only known, the ones who dress up as animals, and the ones who make porn and have sexual fantasies based on anthropomorphic animals.
I might be missing a few facts here or there, but the everyday people you meet who may call themselves 'furries' are usually pretty sane people. It's the extremes that always get the attention, though. Hope I answered your questions!