Originally it was meant as any other fandom, such as pokemon or anime, but for the interest in anthropomorphic characters in art, media and culture. Think disney's Robin Hood, sports mascots, etc. It grew into an entire hobby culture that was completely dominated by art, and similar to how people have online avatars and personas, many furries each made their own character as a way to engage with that interest themselves. Sometimes they would make costumes of those characters so they could basically make a living version of them similar to cosplay but of your very own character. Most common though, which grew astronomically, was depicting those characters in various pieces art.
Even in the early days there were sexual images of anthropomorphic characters, though few, but they were not seen as zoo-resembling unless they were wild or four-legged and were unable to process the knowledge and logic needed to provide consent. Some even used what was called the "harkness test" for such things. Anthro art wasn't seen like that because the characters depicted still had a human mind, as they were either a character from media who had human intilligence to make decisions, or were the equivalent of a video game skin on a real human. For the lifespan of the fandom though, zoos and peds were heavily condemned by literally everyone, because while it was a hobby for the rest of us to make characters and draw them doing stuff, anything resembling real-world events that were seen as sick and disturbing outside the fandom were deemed equally sick and disturbing inside it as well.
To the best of my knowledge and experience, it didn't dominate the furry fandom until much later when the fandom was seen as a safe haven for society's outcasts, those who were bullied, didn't fit in, never had any friends or anyone who understood them, but mostly, a lot of LGBT individuals. It was an outlet. As the fandom prided itself on being "good people" the same way political ideologies do now, the numbers started growing. Unfortunately so did the number of people, often younger, with sick and disturbing minds who started applying porn interest to real life. At first it was all kept private to prevent discrimination and even legal trouble, but the numbers kept growing faster. Even worse, as the world began getting more politcally-driven, so did the super-"accepting" left-leaning fandom, and more focus went toward preventing hatred of sexuality.