Attachment, we are told by all Buddhist sects, is the central cause of suffering. Not the kind of suffering we endure when we have a cold, or accidentally slam the car door on our hand, but the kind of suffering that comes with being a conscious, sentient, being. In fact, the central theme of Buddhism is how to escape this kind of suffering. Methods are numerous. One of the most direct and effective methods involves negating. Psychologically, whenever we interact with something, be it a person, a car, or a tree, a certain kind of relationship happens between us and that object. An attachment if you will. The practice of negation, over time, allows us to experience the world around us without being attached to those experiences. For example, when we see a tree, what we see has lost its properties of tree-ness, its individuality, and this allows us to perceive directly its essence. It is this essence that we call Essential Nature, or that Buddhists call Buddha Nature.
"Neti! Neti!", translated as "Not this! Not this!" or "Neither this! Nor that!" appears in several ancient Indian texts including the Upanishads which formed the early foundation for Buddhsim, Jainism, and Hinduism. The earliest Upanishads are thought to have been written during the 6th Century BC, but verbal transmission could have predated these writings by centuries.
The purpose of this ancient practice is to deny, through continual and progressive effort, everything that is not of Self: in Indian terms, Atman; in Buddhist terms, Essential Self, Dharma, or absolute reality.
In contemporary western vocabulary, we could say that through this method we seek to disassociate the ego from our sensory perceptions, for it is the ego which craves attachments, and it is attachments that bring the ego into existance in the first place.
Before we begin this practice it is imparitive that we truly seek, with all heart and mind and will, to escape from samsara, from a condition of suffering. This practice will not work if taken lightly, if anything short of salvation is considered the objective.
So here is how this practice looks from a practical view. Wherever the mind moves, we observe its motion, and whatever the mind becomes fixated upon we observe this too, and remind ourselves, "not this!". If we look up and see a lamp, we observe the mind's connection with it and deny it: "not this!" If we have a thought about something we did yesterday that makes us feel a certain way, we recognize the mind taking us to this thought and negate it: "not this!". As we are walking to our car, we observe the motion of our feet, our breath, our arms moving and we negate it all with: "not this!".
Eventually, this practice becomes habituated and we don't have to remind ourselves to negate the mind's targets of attention -- it just happens automatically. With time, when all attachments have been severed, the mind becomes primed for an enlightenment experience, an experience where we witness our True Self, our Buddha Nature, the Atman.