Fellow furry over here.
"I don't know what it means to be a furry and I want to."
It pretty much means that you like anthropomorphic (Anthro) animals, though feral can count as well.
The concept of a furry was originally brought up in a 1980 Science Convention when a character drawing was starting up the topic of anthropomorphic animals in Science Fiction novels, the term Furry Fandom didn't come around until 1983.
though most fans in the fandom tend to say that it had originally started before that, when stuff like Kimba The White Lion, Watership Down, and Disney's Robin Hood had came around and in order to separate cartoon animals from real-life ones (Such as Lassie, and Old Yeller) they were simply known as furry animals.
As for when the furry fandom hit up on the internet, I have no idea, but all that I know it's one of the older internet fandoms, and has been around for quite some time.
As for the very vocal dark side, I can only assume that you're referring to NSFW material, of which out of all the fandoms that I've been in the furry fandom has had the most NSFW material, mostly due to how we have Rule 34 (most mainly Digimon, Pokemon, and Starfox) being lumped ontop of NSFW material of fursonas, and others.
And finally on the whole claustrophobic thing, I'd say that it depends on what you wanna post. If it's more on the lines of NSFW then I'd say go over to e621, though if it's SFW then just stick with Furrafinity, Deviantart, and other more common sites.