The philosophical concept of dualism stems from skepticism over the nature of the human mind in relation to the human body. The mind-body problem focuses on the function of the brain and how it relates to consciousness. Plainly stated, philosophers opine as to whether there is a difference between the brain and the mind. Dualists believe the mind is a separate entity from the physical brain.

The proponents of dualism generally agree that the mind is a non-physical substance having a separate existence from the physical body. Substance dualism favors the notion that the mind is a thinking entity without physical properties. Property dualism contends that the mind is simply a non-physical property of the brain. While both positions recognize a difference between the physical matter of the body and non-physical properties of the mind, substance dualism more closely defends the overall concept of dualism.

There is a great deal of scientific disagreement with the concept of dualism, but dualists contend that humans are made up of both a complex physical organism and a separate non-physical mind many refer to as the soul. This view squares with the philosophical position advanced by substance dualists. Property dualists are more closely aligned with the philosophy of materialism, the view that mental processes depend on matter, since nothing exists without matter.

Science has progressed through the centuries without a definitive explanation of the nature of the mind in relation to the body. Substance dualism theoretically provides us with the possibility that there is a greater explanation of the relationship between mind and body than physical science provides.

Substance dualism holds that there are two kinds of substances or two states: The physical is all the material, matter.  The mental is non-physical; it has no spatial extension; the mental, or mind (not to be confused with brain, which is physical) exists but somewhere immaterial (abstract consciousness, soul, etc.)  The mental state exists and can causally affect the physical world, but the mental state is abstract and therefore external to the physical world. 

Property dualism holds that there is only one type of substance but two kinds of properties which inhere in that substance: mental and physical.  There are different versions of PD but the general idea is that mental properties, emerge, arise or are produced by/from physical properties.  Mental properties can be reduced/explained by physical states or they cannot.  But, property dualists do hold that there is an ontological difference between mental and physical properties.  Examples of properties: redness, spherical.  These properties inhere in/on physical properties but, isolated, what/where are they?  Thus, they have a quality (property) that is ontologically different from the physical properties and states in which they inhere.  Property dualists believe that the consciousness is a property which inheres in a brain as red inheres in an apple. 

Analogously speaking, if you think red can exist without inhering in anything then you are a substance dualist; that is, red (consciousness) is not just a property.  It is an abstract something that exists somewhere/somehow else and it can manifest through or affect some physical thing.  If you think red needs the apple or emerges as a property of it, then you are a property dualist.