Non-duality is a way of speaking about and underscoring the spiritual unity of all things. So, for instance Divinity or the divine reality in which all things originate is the same spiritual reality that is the essence of human consciousness and identity. Or to put it in another simpler and traditional way: God’s spirit and man’s spirit are one spirit.
The non-duality concept is also a way of underscoring how the mind functions in relation to the phenomenal world and the need to use but transcend the mind-level of understanding. The mind divides things, separates them, and understands in terms of relationships between different phenomena. The light of spiritual reality shining down into the mind sparks the non-duality realization, and a strict non-duelists might assert that all I have written here is itself too dualistic, and it is because any analysis of relationships involves duality or multiplicities that mislead as words, to some degree, inevitably do.
Another example is that in very dualistic thinking—such as we find in most religions and philosophies, spirit is conceived of as separate from matter. But a more non-dualistic concept is to define spirit and matter as aspects of one thing—in other words there is only single continuum of spirit-matter.
For your edification and amusement I point to the follow video on this theme:
Mystic Muse 