Furry art is art catering to a specific fetish of animals that are given human features. It's a fandom that revolves around the worst possible combination of guilt free bestiality combined with OC DO NOT STEAL neon colored mary sue persona BS.
So if it's basically a cat or dog or parrot or dinosaur with a speech bubble slapped onto it with rainbow fur/feathers/scales then it's furry art. But everything in this thread is "real" mythological creatures, like the classic devil, fawn, pan, satyr, "real" fictional characters like Beast or Beast Boy, etc. etc. etc. Think of it like this, if it's an old school picture made with real oil paints (or at least if it mimics that style like all the art posted in this thread) of a centaur fucking a mermaid then it's ok. But if it's "art" that looks like a My Little Pony screencap that's been shopped to have sex in it then it's furry art.
It's more about the fandom, really. Once they get a foothold into a specific board then they grow like cancer and it's almost impossible to get rid of them.