Substance dualism is a fundamentally ontological position: it states that the mental and the physical are separate substances with independant existence. Physical things are extended in space and do not possess any thought. Mental things have thought as their very essence, but do not have any extension in the physical world.
Substance dualism is a position favoured by various religions, because the distinct mind can easily by synonymous with the soul. Plato was similarly a substance dualist, believing that the soul inhabits the body temporarily, and otherwise exists in the infinite metaphysical realm of the forms (or rational knowledge).
Opposed to substance dualists (aside from monists) are property dualists, who argue that the mind emerges from the arrangement of the physical as a property of it. Property dualists also place an ontological distinction between mind and body, but deny that they are separate, independant substances.
See: mind-body problem