Advaita Vedaanta explains the creation of the world by the theory of vivarta. (…) According to Advaita, the effect is not an actual transformation of the cause. Brahman is immutable and there can be no transformation of it. It only serves as the substratum (adhishThaana) for the appearance of the universe, just as the rope serves as the substratum for the appearance of the illusory snake.
This appearance of the universe is due to avidyaa, or nescience, which conceals Brahman by its veiling power (aavaraNa s’akti) and projects the universe by its power of projection (vikshepa s’akti). The universe is therefore said to be only a vivarta, or apparent transformation, of Brahman. Like the illusory snake with rope as the substratum, the universe is illusory, or mithyaa, with Brahman as the substratum.
But there is a vital difference between the illusoriness of the rope-snake and that of the universe. While the snake is purely illusory, or praatibhaasika, the universe has empirical, or vyaavahaarika, reality. That means that the universe is real for all those who are still in ignorance of Brahman. It loses its reality only when Brahman is realized as the only reality and as identical with one’s own self, or, in other words, when identification with the body-mind complex completely disappears.
Bondage is nothing but identification with the body-mind complex. This identification being due only to the ignorance of the truth that one is really the aatmaa, which is the same as Brahman, it can be removed only by the knowledge of one’s real nature as Brahman.
Vedanta Spiritual Library | http://www.celextel.org/ Elucidation of Terms and Concepts in Vedanta [Based on the Commentaries of Sri Sankaracharya and other authoritative texts] By S. N. Sastri