What is a soul exactly?

Various religious traditions and philosophers invoke the notion of a soul. It may be that I am to be identified with a particular soul and that when my body stops working properly my soul will ascend to Heaven. But what exactly is a soul? Many philosophers argue that souls must not be physical and that souls are the "subjects of consciousness." This simply means that my soul is the thing doing the thinking, but it's not a "thing" in the traditional sense. It's not a physical thing like a pen or gland in my body. OK. So it's a non-physical, thinking thing. But what exactly are we talking about here? I think there are some non-physical things like, perhaps, concepts (e.g., justice and multiplication) and fictional things (e.g., Harry Potter and Luke Skywalker). But souls appear to be something quite different from the sorts of things that I think are real and which are non-physical. My soul isn't just a concept and it's presumably not a fictional thing. Does anyone have any thoughts about what a soul is exactly? It would help if there were an analogous immaterial thing that would help shed light on souls, but it's difficult to come up with a satisfying example.

UPDATE 12/8/11: A kind reader of the blog emailed this short peice written by Bertrand Russell.