What is the appeal behind being a furry?

Let me answer this question twice.

Firstly, there are many different reasons someone might want to fursuit (dress up in a big animal costume). For some, it's a way of playing a character and showing off their creation, thus it will have the same appeal as acting might have for someone else. For others, it's a way to behave in a different (usually more confident, silly, childlike, or outgoing) way than they usually would, so has the appeal of being able to act in such a way. And again, for others it's a case of interacting in different ways with people and making them smile (take a woman's purse and watch her go nuts and phone the cops, do the same thing in a raccoon suit and she's more likely to giggle and film it). And for many, it's a combination of these things and possibly several others.

Now to further answer the question about generally being a furry. It involves a lot more than just fursuiting, and while that's probably the most visual aspect to people outside of the fandom, it's not the biggest aspect within it. Indeed, only around a quarter of furries own a fursuit.

So other appeals might be a love of art; enjoyment of the amazing community; being a fan of comics and stories; and a million other things.

Ultimately though, it all boils down to one thing: fun.