Welcome to the FF!
Hope you enjoy it here.
I really wouldn't call being Furry a "movement"...it's just what someone is.
My definition of a Furry would be someone who has an interest in anthropomorphic (anthro) art, RPing as an animal, and/or animals in general. (Anthropomorphic is when there are human-like characteristics applied to an animal like walking on two legs, talking, etc.) Basically, the only goal we Furries have is to be accepted and for others to understand us since a lot of people think that all Furries are just interesting in yiffing all the time, which isn't true, what a Furry likes depends on who the Furry is.
There are several definitions of what a Furry is, it just depends on who you actually ask. You'll most likely get some other definitions of what a Furry is from other members, but I hope I've helped you understand at least a little bit more.