Worded even more succinctly than my rambling did! It's a loaded question, one that has a lot of answers that may all be wrong for what we currently know.
I would call myself an agnostic, and I suppose I believe in a soul... In that they are a (potentially inaccurate) way of describing the singularity of oneself.
We contain something which has conscious thoughts, and awareness of "itself" while existing. I suppose that would be a soul, no? We can remember and have individual lives with isolated moments no one else will ever know. Are those memories really only random creases in our brain? Do the feelings and deeper experiences for you wash away as nothing alongside the mechanics of those memories? What makes us... well, us?
I like to think the soul is just that, the part of ourselves that is truly unique, and can only fully be witnessed internally. The part of you that is only ever going to fully exist in the here and now, while still recalling the there and then. That which gives us the full breadth of emotion tied to deeper thought, and hopefully some understanding. That, at least, is a miraculous thing to get to experience... spiritually or not.
The immutability of a soul is a different question, one which we'll get an answer to after the physical living stops.