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 and property dualism are philosophical positions that address the age-old mind-body problem and the question of consciousness. Property dualism argues that mental (mind) properties are distinct from physical (body) properties, but that both mind and body are made up of the same substance. In essence this idea claims that we can understand mind if we come to fully understand the function of the brain.

In contrast, substance dualism argues that the mental (mind) and the physical (body) are two distinct substances; that they are fundamentally different things. Further, substance dualism asserts that understanding one does not necessarily allow us to understand the other. Substance dualism might be properly called "classical dualism". René Descartes was a proponent of substance dualism, arguing that mind (the res cognitans) and body (the res extensa) were two distinct things, and that one would never be able to fully understand the mind in material terms. He held this view in part to defend the idea of the immaterial, immortal soul. His ideas laid the foundation for the mind-body problem, which has challenged scientists and thinkers since the early modern era.

Most contemporary scientific understandings, such as those one finds in modern neuroscience, are expressions of property dualism, which is arguably a variation on materialism. In this sense, substance dualism is the strongest expression of dualism writ-large, since it asserts a fundamental difference between the material (body) and the spiritual (mind and/or soul).

According to the concept of mind-body dualism, our minds possess an aspect that is nonmaterial aside from the physical. This aspect is the spiritual dimension that includes our consciousness, thought processes, knowledge etc. Thus, in dualism, the mental and the physical are both real.

Various types of dualism exist: substance, property, and predicate dualism. 

Substance dualism posits that the mental can exist outside of the body. That is, the mental and the physical are two totally separate entities. For instance, intensive studies on the brain may not lead to a complete understanding of the functioning of the mind. A substance is characterized by its properties. A substance owns its properties.

Property dualism, on the other hand, posits that there exists only one kind of substance with different properties. For instance, a substance such as a brain has two different properties: physical and mental. Thus, in order to understand these properties, one simply has to study the brain.

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.