Basically, there are people who like to draw or imagine character that are anthropomorphic (animals, but with humans traits). Most of the time they like to draw those characters or even get a furrsuit to disguise as them.
That's what it is at the base. The problem is that, like every community, sh*t happens. But with furries there's alot to talk about.
But that doesn't mean every furries are bad. There's still people, normal people.
Actually, you can find a great variety of people here, for the best, or for the worst. So don't judge too quick a furry, in fact judge them like a normal person. But a general advice would be to stay out of furry content, unless you're sure on what you're doing into (personal advice).
Here's the silly problems:
So, firstly it's hated because so people act really cringely. Usually it never hurt anyone. It can be for silly art to slang that should stay in the furry circle, like weird RP.
Also, because the group is mostly hated, some people like to victimize themselves too much, and put people in embarrassing position.
And there's also the problem of the guy that makes "the furry Fandom" their whole personality but this point and the earlier one are common community problems.
Lastly, some people just don't like anthropomorphism. That it.
Here is the mature part, skip if you don't feel comfortable with that type problems:
Because it's (mostly) an artist based community, they doesn't escape of the NSFW problem (basically, sex). That tarnished their reputation ALOT.
Speaking of that problem, some very influent furries were revealed to be z*os. Basically predators, but for animals instead of children. Most furries are against it now, but those dramas will be really vanish, because drawing anthropomorphic creatures is for some already a sign that you're a z*os