A furry, at its base, is a fan of anthropomorphic animal characters (or "anthros", as it is commonly abbreviated to). The majority of the fandom consists of people who enjoy fiction and art revolving around anthropomorphic animal characters, ranging from independently written stories and comic books to established, mainstream franchises, with Sonic the Hedgehog, Teenage Mutant Ninja Turtles, The Lion King, and Zootopia being some of the most revered mainstream works.
The furry fandom got its start in the early 1980s, with Albedo: Erma Felna EDF and its related works generally considered the first "furry" comic book. The immediate success of the independently produced Teenage Mutant Ninja Turtles in 1984, as opposed to corporate works by Disney et al, enticed publishers and creators into making more works starring or exclusively featuring anthro characters; this opened the doors for actual furry creators to get their works circulated. Written works began to excel during this time as well thanks to fanzines, as well as a growing presence of written and drawn works appearing at science fiction and fantasy conventions. By 1989, furry conventions began appearing, with some (such as Midwest FurFest and the now-discontinued ConFurence) branching off from already established sci-fi and fantasy conventions. Currently, there are over 80 established conventions and gatherings worldwide (with the United States holding seven of the ten largest in the world), countless meetsnote and several websites dedicated exclusively to furry art, literature and even clothing and accessories.
Many, but not all furries, generate what is known as a fursona (a "furry persona") by which they express themselves or self-actualize. Exactly where on the Sliding Scale of Anthropomorphism these characters are doesn't matter, as they can vary from extremely cartoony to hyper-realistic; the majority of them tend to be on the anthropomorphic side, though non-anthro fursonas (referred to as "Ferals") are popular, too. The term "Furry" is a bit of a misnomer as characters based on birds, reptiles (referred to as "Scalies"), amphibians, and even non-tetrapods are also counted under the umbrella term. While originally used as characters in comics and stories, fursonas are now generally created as a means of self-expression. As a result, the furry fandom differs from comic and anime fandoms by its emphasis on pet projects of original work and on commissioned artworks of personal characters, rather than focusing exclusively on published works.
The most visible part of the furry fandom are fursuits, mascot-style costumes of original characters. Much like cosplay, fursuits are labors of love, and there are many home-grown costume businesses who sell original or commissioned full or partial costumes. A common misconception is that a fursuit is a requirement in the fandom; in reality, roughly a quarter of the fandom actually own one. There are several other scenes within furry: artists, crafters, writers, puppeteers, and most recently, dancers and performance artists, have all found a space within the fandom to share anthro-oriented work.
Another small though highly visible section lies those with literal anthropomorphic animal fetishes, including an even smaller subset of erotic cosplayers and other individuals who take their kinks beyond the computer screen. Though there's plenty of kink-based artwork and literature out there in many fandoms, it's this smaller subset that has gotten plenty of attention and vilification. MTV, CSI, ER and Vanity Fair, amongst others, have all had their moments covering this controversial side of the fandom. The effects of this period of mainstream coverage around the Turn of the Millennium are still leaving ripples throughout mainstream discourse of furries: while it is very easy now to be "out" as a nerd, otaku or comic book fan, it is still possible to be ostracized both personally and professionally for being "out" as a furry. The crude fallacy of "all furries do that yiff stuff" also led to a strict distrust of the media among furries until very recently. Nevertheless, this "anti-furry" attitude has chilled thanks to both the Law Of Fan Jackassery and to recently changing social attitudes, thanks in no small part to the intermingling of fandoms in social media.note
In terms of demographics, the median age of the fandom currently skews younger thanks to the Internet, but there are members of all ages. Nearly all furries have hobbies that extend outside of the fandom: gaming, anime, sports, cars, outdoor exploration... name it and you'll probably find some furries there, too. There's also a propensity for sarcastic, self-deprecating humor as a reaction to all of the unfortunately biased media coverage of the past decade.
Also, meet Dr. Kathy Gerbasi, social psychologist who has created peer-reviewed studies of the fandom since 2006.
All done! Now don't you just have a warm, fuzzy feeling?