It may have something to do with keeping connected to your fursona, but then again, I'm either a red panda, or a lynx, so I don't know for sure, so neither of those animals even wear collars!
That aside, Its somewhat of a fashion statement, saying "I'm not afraid to show who I am", but to a point, its like trying to pass a message on.
When people ask me why I wear my collar, I usually respond with "Personal reasons," or "trying to make a statement". Their responses "How can you make a statement if you won't tell somebody what the statement is?
The statement, is that you're a fur, yes, obvious. Though, to some, or some that aren't quite as open as I am around friends, he or she might keep to themselves. If the person wondering has any curiosity, or the guts to ask, he or she will. This happened once.
Random girl: "...are you a furry >.<?"
Me: "yeah, actually, I am"
Her: "so am I >.<!!!!" *Runs away*
Never saw her again, but oh well