What is it that you feel that you are, truly? What are you inside the meat shell? Most of us have some conception of what that might be, be it a soul, a mentality, or what have you.
“Otherkin” is just a word referring to this feeling, that one’s form or nature is not the same as their meat shell / body. That the body is a vehicle, and that they themselves are something else. There are a variety of things that you might be, besides simply “a soul” or “a mentality”, but I’ll leave that to your imagination. (And web browsing.)
At its root, “otherkin” is referring to this idea that we, the essence of who we are, is something different than human. You might consider these other things to be metaphors or yearnings, or something factually true, but it is what it is, and it is undeniable that most people do feel this way, even if they don’t put a name to it.
This is not strictly related to plurality, though I’m sure you can see how the two concepts could come together.
In the case of Feathersong, two of us consider ourselves to be “fae” (the fairy tale kind, not necessarily the little people with wings kind), and the other of us considers herself to be “celestial” (think made of star-stuff, a little like an angel, but less religious).