There are five different words in Hebrew that are generally translated as soul...so it is more complex than most people realize...but essentially we ARE a soul, and our physical bodies are merely vehicles our souls use to interact with the physical world.
If you remove your body and brain...you do not cease to exist, but we have the potential through God to elevate our souls far beyond the most basic. The lowest degree of soul (nefesh in Hebrew) is actaully attached to the body (in the blood-hence the levitical prohibition on drinking blood) and is usually refered to as "animal soul". The nefesh expires when the body does (sorry...no animals in heaven). Next is Ruach, often translated breath or wind. Humans, obviously, have more than just the nefesh or animal soul as we are eternal beings not bound only to the physical.
Is this what you wanted to know? I will stop here in case I am not really helping...maybe you can be more specific with your question?