The concept of ajñāna is most funda-mental to Advaita Vedānta. In fact, it can be rightly called the cornerstone upon which the mighty edifice of Advaita metaphysics stands.
Ajñāna is not so much ‘ignorance’ or ‘nescience’ as ‘non-knowledge.’ It successfully prevents knowledge from arising. Once knowledge does arise, ajñāna just disappears! Rooted in jñāna or consciousness as its locus, it unfolds its charms and spells.
An oft-quoted illustration given in the works on Advaita Vedānta to explain ajñāna is that of the rope appearing as snake (in insufficient light) and nacre appearing as silver (in moonlight). It is ajñāna that is responsible for this appearance. Since the snake and silver are actually perceived—unlike the son of a barren woman or the horns of a hare—they are not asat (unreal). Since they disappear on the rise of the knowledge of their substratum viz., the rope and the nacre, they are not sat (real) either. Hence ajñāna, responsible for this phenomenon is described as sad-asad-vilakṣaṇa, (different from both the real and the unreal), just as the neuter gender is different from both the masculine and the feminine genders.
This ajñāna is said to be bhāvarūpa (existent) since it is experienced as indicated in such statements as ‘I do not know anything’ or ‘I am ignorant;’ or since it does not cause the rope and the nacre disappear completely from view. It is endowed with two śaktis or powers viz., āvaraṇaśakti (veiling power) and vikṣepaśakti (transforming power). It veils the true nature of rope and nacre and shows up snake and silver in their place by apparently transforming them.
Ajñāna at the cosmic level is termed māyā and is often identified with prakṛti (nature) with its three guṇas sattva, rajas and tamas. At the individual level it is more commonly called ‘avidyā’ and is held responsible for the apparent limitation of the ātman (the Self) as jīva (embodied being subject to transmigration).
In conclusion it can be said that in Advaita Vedānta, jñāna refers to caitanya or pure consciousness which is one and infinite. Hence a-jñāna is that phenomenon which makes this infinite appear as many and finite.