So, the definition of "furry" is someone who just appreciates anthropomorphic animals (characters from movies like Zootopia are examples of socially accepted furries). The bad rap leaves people thinking being a furry = you like beastiality, which is absolutely not the truth. Furries have been around for a long time, though most folks today just like to dress up and design characters they feel represent themselves, the kinky part definitely exists too.
https://www.flayrah.com/4117/retrospective-illustrated-chronology-furry-fandom-1966–1996 can check out some examples here throughout history
For me, I feel like I've always been a furry. I never really told people about it because I know how most of society views furries because of the misinformation. As for my family, I think my sisters know, but it's not really like a sexuality where you'd just "come out." haha. so, if someone were to ask me if I were a furry, I'd say yes, but I'm not going to go around saying I am, if that makes sense. I've never been to a convention before (as I don't own a suit yet, and don't particularly want to go without one), but I hear the general community is friendly and welcoming. I don't know for sure, as I don't interact with many of them and don't have any IRL friends that are furries. It does get hot in-suit and most of the suiters I know are OK with revealing their identities- really, every furry I've interacted with is fully understanding that it's just a costume, and that it's just a character. We know we aren't ACTUALLY dogs. In the furry fandom, everyone has a "fursona," like, persona, the main representation of you. Mine, for example, is a fox. I designed her myself, and I can't say the connection is spiritual or anything, it's just what I envision myself looking like if I were an animal. Mine is pretty boring compared to some. You can be as creative as you want. I've seen some really original and super cool fursonas, with 4 arms, or a mouth at the end of their tail, or big wings, or a mixture of a bunch of animals, etc etc. That brings me to answer your last question- the demographic.. I would say it's pretty diverse. I've seen 11-year-old furries, I've seen 45-year-old furries, and I think it's because of the freedom and creativity with expression that appeals to all ages. I hope this helped some.