At any stage of a path, one can experience non-separation from what is - non-self. This can be developed using any methods that you find effective to increase awareness.
Nonduality has various meanings and is an overall term to cover various approaches, including Advaita and Emptiness. It primarily labels the experience of non-separation and non-distinction when it arises in daily life. People can be thrown in to that state with "sudden awakening" (satori-like events) or grow in to it through "gradual awakening". The word explicitly does not refer to final emancipation or liberation, because most writers agree that people develop beyond nonduality.
As a philosophical perspective, this quote from Mariana Caplan's book "Eyes Wide Open" is ideal:
Ngakpa Chogyam, a Tibetan Buddhist teacher from Wales, offers a perspective on nonduality that includes all of life as a direct expression of the nondual core of truth. He explains that nonduality, or emptiness, has two facets: one is empty, or nondual, and the other is form, or duality. Therefore, duality is not illusory but is one aspect of nonduality. Like the two sides of a coin, the formless reality has two dimensions -- one is form, the other is formless.
When we perceive duality as separate from nonduality (or nonduality as separate from duality), we do not engage the world of manifestation from the perspective of oneness, and thereby we fall into an erroneous relationship with it. From this perspective it is not "life" or duality that is maya, or illusion: rather it is our relationship to the world that is illusory.
Nonduality is the occurrence of non-self.