Non-Duality is a way of experiencing life that is beyond the holding of any belief about it. It points toward a liberation of the attachment to a separate "me" and this brings psychological freedom and peace. When consciousness gives up duality as a way of looking at the world it feels alive by simply Being, as opposed to being caught in the complexity of "thinking". There is an intuitive recognition that underneath all appearances there is One spacious consciousness that contains all of life and that each of us at the core is that spacious consciousness. When consciousness awakens one sees directly that the human sense of separateness and uniqueness is an identification with the body and conditioning that limits understanding of what we truly are.
Most of us can understand upon reflection the inter-connectedness of all things. We can see that without air, water, the trees and many other gifts of nature we could not exist as a species, and we can see that all of humanity shares the same needs and the same connectedness as part of nature. Our bodies are natural expressions of life. As Kahil Gibran once expressed poetically "Our children are life's longing for itself". So our existence is this expression of life as human, and our uniqueness is part of the unfolding of nature's many variant ways, greatly colored by our unique heritage, conditioning and energetic styles, intelligence, inclinations, talents, etc. How natural it is for us to identify as "This".
But non-duality is not about an understanding of our position in the world, even of our interdependence. It is an invitation to a direct intuitive remembrance of ourselves as this essence of life, before all the experiences and conditioning were attached and our thoughts became the apparent managers of our lives. It implies that as soon as thought and mind become active, all is divided, all appears to be dual -- birth and death, awake and asleep, myself and another, light and dark, like and dislike, good and evil -- all are the conclusions of the independent mind, which finds its way in life through division. To be enlightened is to be undivided, while still living with the paradox of division.
The mind cannot understand non-division. It assumes that the gathering and organizing of facts or memories or experiences is essential for navigation in the world. And to some degree this is true -- the rules for the world of form require certain understandings of boundaries (e.g. I cannot physically fly off of a building, I cannot ingest poison if I want to stay embodied, I can learn to drive and operate machinery, I can set up time in days and months and years, etc.) Non-dual teachings however, are not about the world of form. They are about the wholeness inherent in the absolute, in that which precedes and follows form, and which is the essence itself that allows form to appear. They point to Oneness, wholeness, awareness, presence, consciousness, beauty, love... all as the essential Truth of existence. Our deepest source within, our own Awareness, already knows Itself to be This. But we are so distracted by the world of form, and the content of mind, that most people most of the time never feel or touch intimately what they really are. Non-dual teachings, or in some cases the presence of an awakened teacher, exist in order to disturb or startle the thought patterns out of their complacency and delusion long enough for the true nature to be remembered.
Although many non-dual teachers appear to be saying that thought must stop or will stop if one is enlightened, this is not a fact to be feared or used to imply one becomes helpless and limited upon waking up to reality. What a waste of potential that would be!
These expressions are pointers beyond the limitations of thought, much as pointing to the moon does not mean the abandonment of the earth. To reach outer space astronauts have to leap out of the environment of earth -- have to be willing to live in the vastness of open space and trust their survival. To awaken to our true nature we have to similarly reach deeper than mind, into the empty-of-thought openness that is pure awareness, before thought-forms enter the stream. So it is no-mind as we perceive beyond mind. It has been called the dissolution of mind, but it is closer to a transparency, a seeing through the illusory, transient, conditioned and generally irrational nature of thought. As we recognize our own impermanence, and how we have been attached to ourselves as a unique but transient character formed by belief and experience, we take ourselves and others less seriously, so we become less compulsive and ego-driven. The ego has no power unless it believes all of its thoughts. The ego is the movement of attachment, and it gradually falls away when the Truth is seen and lived. When thoughts and even feelings are seen as energies moving through a system rather than "who I am", we cannot easily sustain a belief in the separate self.
Why should people invite themselves into a process leading to a lack of identification with the separate self? At first glance this would seem psychologically and emotionally unhealthy. During some stages of awakening it can certainly be frightening and disorienting, and one must persevere through the fear. But many people feel driven to make this journey, and others fall into the realization spontaneously. It is a longing to know our natural state of Being, a longing to know our "source" and end the sense of alienation in an ego-driven world. It is sometimes felt as a longing to know if there is a god, and of what nature it is. It is also the only way ultimately to feel at peace with life and death, and to end the inner turmoil that comes with division and the search to know what matters, what is real. When we clearly see the separate self as a simply a dance of energies in a creative movement of nature, and we allow what we experience to flow through without struggle, our lives become more free and more immediate. Living in the moment brings more joy than planning for the future or dwelling on the past. Life becomes more simple and more intimate and more relaxed.
If everything I write or other non-dual teachings offer are simply taken as beliefs, they are just as sticky as any other belief, just as liable to trap you in mind, just as lacking in Truth. They are no more useful than a picture of ice cream is able to satisfy your craving for it.
In the end non-dual teachings, or sitting in silence with a teacher, are aimed at driving you inward to question and discover your own realization of Truth, beyond your mind and beliefs and assumptions and feelings, in the stillness there, discovering within yourself who you are.