Since the rise of science we've come to see the soul as a purely religious concept, but it arises naturally from how we perceive the world around us (see Descarte's Baby). This Mind-body problem has been debated since the beginning of philosophy. Dualism sees the mind (or soul) as a real thing, distinct from the body.
A major reason why there has been little progress in understanding (until recently) is that how the mind actually works is very different than how it seems that our mind works (see The User Interface Analogy, Unconscious). Mind/body dualism just makes sense. Descarte's Baby argues that young children instinctively develop an dualistic theory of mind. Why is this? You could say that dualism is the design philosophy of the user illusion.
By means of Level Confusion, dualism has become thoroughly entwined with views about whether mental entities such as thoughts, feelings and intentions are real or not. Our mind is implemented by our brain (and body), so cannot exist without it, but mind is an emergent property which is not nearly as constrained by its physical substrate as traditional arguments have supposed. This ultimate dependence of mind on a real physical substrate proves nothing about the reality of mental phenomena.
See also The Interpreter Theory, Intentional Opacity.