Yeah, not a new concept by internet standards, older than a lot of the people on here. I think the first convention was in the mid 80s, so I guess that'd be when we can say it got popular.
I think it can be traced back to the early 70's with various underground comics, but ground zero was the Disney Robin Hood and Fritz the Cat. From there it slowly grew, Thundercats, Lola Bunny, Animaniacs' Minerva Mink, Tiny Toons characters, etc...
I'm older than most of y'all but first got online in the early 90's. Furries and furry fandam were already popular online. But you never heard of or encountered it outside of the internet.
I'm assuming the fandom existed before that through zines and meet ups and stuff like other fandoms and subcultures did.
I think it seems bigger or newer just because more people are aware of it now and it's a known enough thing that it shows up in TV shows and movies.
And people doing sexy fan art of anthro characters or writing erotica about them is older than the term "rule 34." I remember seeing sexy drawings of Minerva Mink and Maid Marion back then. I think it was like a decade later when the internet rules meme happened.
It all started in ancient egypt if not earlier still. 1985-2003 was the peak of furry content in the mainstream Disney afternoon shows (Gummi Bears, Ducktales, Talespin, Rescue Rangers, etc.) Animaniacs Sonic (mostly the comics) Spacejam Pokemon Digimon Starfox Howevermany Disney movies Indie and underground comics And too many others to count, it was a Golden Age.
The community has existed for a long time, but was popularized by characters like Lola Bunny in the kid 90s, and then even more so by the influx of weirdly sexy anthropomorphic characters such as Rouge the Bat in the early 2000s.