Dallas Willard, Thomas Moore, David Benner, Richard Rohr and a few other folks have taken a first pass at this topic. In light of my time spent immersed in their books and ideas, I had my graphic designer friend, Jeff, create the below image. As I have taught this image to others, I have been shocked at how helpful it has been for people.
So, in light of this image, here's a quick answer to: What is a Soul?
Try it. Put your thumb on one of these dimensions symbolizing that that dimension feels a bit heavy or out of sorts today. Now look at the other dimensions - how are they affected as this one dimension is a bit off. Do you see it? These dimensions are profoundly interrelated.
For now - this is a good start at naming what the soul is:
It is the essence of who we are that is influenced by six interrelated dimensions.
What is the state of you soul today?