From the Science and Nonduality Website
Nonduality is the philosophical, spiritual, and scientific understanding of non-separation and fundamental intrinsic oneness.
AND FROM WIKIPEDIA
Nondualism is a term used to denote affinity, or unity, rather than duality or separateness or multiplicity. In reference to the universe it may be used to denote the idea that things appear distinct while not being separate.
Our starting point is the statement “we are all one,” and this is meant not in some abstract sense but at the deepest level of existence. Duality, or separation between the observer and the observed, is an illusion that the Eastern mystics have long recognized and Western science has more recently come to understand through quantum mechanics.
Dualities are usually seen in terms of opposites: Mind/Matter, Self/Other, Conscious/Unconscious, Illusion/Reality, Quantum/Classical, Wave/Particle, Spiritual/Material, Beginning/End, Male/Female, Living/Dead and Good/Evil. Nonduality is the understanding that identification with common dualisms avoids recognition of a deeper reality.