What is Nonduality?
Nonduality is the state or condition of not being separate and distinct even if appearing to be so. It is the condition which allows us to say that there is no true separation between ourselves and anyone else or anything else in the world, for instance. When we say things like “We are all one,” or “God is in all things,” we are asserting that the presence we call ‘reality’ is a nonduality.
A “nondualism” is a systematic description of nondual reality, or the tradition of spiritual practices of nonduality.
More Complicated Answer:
Nonduality is the condition that one arrives at when all distinctions and relations between ‘things’ are removed. Fundamentally, all such distinctions and relations are the result of error on our part because it is we that impose the idea of plurality on the whole. Nonduality is thus a simple wholeness, rather than an “all in one” whole. It is very difficult to clearly contemplate such a simple wholeness, because by thinking about it and conceptualizing it, we have lost the simple wholeness that is the real nonduality that we were trying to grasp, which is always already our very nature – we are reality. Nonduality is the Infinite because we can both indivisibly apprehend it and enumerate it inexhaustibly into parts and relations between parts.
Nondualism according to this understanding is an error because fundamentally anything that we say or think about the Infinite removes this simple wholeness of reality from our grasp.
The Ultimate Answer:
Nonduality is ineffable. Any words that attempt to capture its essence instead hides it from us.