In that thread on the other board, Advocatus said:
I don't know what Cherokee has in mind, but Carl Sagan used to like the word "spiritual". The word originally meant "breath", and by extension it still refers to "whatever keeps you alive". In that sense, "spirit" is the essence of being Human, our capacity for thinking in abstract ways, our capacity for seeing beauty in the most unlikely places, for getting excited about things, for pondering questions that don't have answers, for being passionate, for caring. All that is "spirituality", in my opinion, even if it doesn't come from a supernatural source.
I couldn't put it any better than that. I don't believe we have a "soul" or a supernatural "spirit," but that has nothing to do with feeling wonder or being struck by beauty or anything else that distinguishes humans (and possibly chimps, dolphins, and others) from other animals.
In the sense of meaning "that which is life-affirming" (which, by the way, is also a central tenet of objectivism - doing that which is life-affirming), the feeling of having spirituality is not supernatural.