Dualism (a form of pluralism) in philosophy and science primarily refers to matters of mind and consciousness, deriving from the subtly different forms of dualism described by Plato and Aristotle, sharply refined by Rene Descartes' substance dualism of the seventeenth century. Dualism affirms that for any particular domain there are two categories of causation derived from two fundamental principles [i.e., "The mind-body" problem].
The question dualism addresses in the realm of philosophy of science has to do with the apparent comprehensibility of the world, and whether there are in fact two classes of phenomena - material and immaterial. While a strict materialism or physicalism would consider mind/consciousness to be an epiphenomenon of matter and its complex processes [Matter causes Mind], a substance dualism rejects the reduction of all things to deterministic atomic processes, instead asserting that immaterial Mind determines the reality of things according to its ability to comprehend things [Mind causes Matter].
These two distinct schools of scientific philosophy are reflected in the different approaches to quantification of consciousness, as classical/materialist (a.k.a. "Emergent") phenomenon of complex matter/energy field interactions, or as observer-determined measurements of quantum level superpositional states. British mathematical physicist Sir Roger Penrose offers a modification of the quantum level interpretation through his "Orchestrated Objective Reduction" theory [Orch-OR], postulating that reality itself causes reduction of wavefunction in the broad milieu by collapsing a space-time superposition that reaches Planck level intensity by the action of quantum gravity. This model allows for a "habit" of matter to recreate itself in the following instant of time (measured at Planck level, instanton - a distance unit) what it was in the previous instant of time/position in space [see: Space-Time, Collapse of Wavefunction].
In theology, Dualism refers to two eternally opposed and coexisting principles, usually described as good and evil, light and darkness, yin and yang, or some other pair of conflicting principles.
Web Resources On Dualism
Dualism in Stanford Encyclopedia of Philosophy
Dualism in Catholic Encyclopedia
Book Resources On Dualism
Case for Dualism by John R. Smythies
C.S. Lewis's Dangerous Idea: In Defense of the Argument from Reason by Victor Reppert