These terms can be understood as follows:
Advaita Vedanta says that ignorance of Brahman has created this world.
Ignorance, which is the opposite of knowledge (jnana-virodhi), is not
something negative. It has a positive character (bhavarupa).It has two
powers: (1) the veiling power (avarana-shakti) and (2) the power of
projection (vikshepa-shakti). Ignorance has the power to cover or veil the
Reality, which is Brahman, and also the power to project this world on
the veiled or covered Reality.
The world is the product of mula-avidya. The individual ego, which is
part of this world, is also the product of mula-avidya. Consciousness
associated with this ego is called the Atman or the Jivatman. Between
the Jivatman and Brahman (Paramatman) there is a thin veil of
ignorance. It is like a cloud that does not allow an individual to see
the sun. In this analogy the Brahman is the sun and the patch of cloud
is the ignorance of the individual. When this individual’s ignorance
is dispelled by the knowledge of Brahman, he or she will have the
experience of Brahman.
From the point of view of Advaita Vedanta, maya and avidya are the
same. Just as avidya or ignorance has the powers, as it were, to hide
Brahman and project something else, such as the world, on it, so also
maya, as it were, can cover up Brahman and project the world onto it.
Maya cannot really cover the Reality that is Brahman. A patch of cloud
can never cover the sun. It only covers the eyes of those who are
looking at the sun. In the same way maya covers our knowing ability
and thus obstructs our knowledge of Brahman.
In any act of knowing, the ‘knower’ and the object known’ have to be
separate from each other. They cannot be the same. In order for us to
know maya, it has to be separate from us. Individuals like us are the
products of maya and we are all posited within the domain of maya.
Maya and we individuals are not separate from each other, just as
chocolate and a bear-shaped chocolate candy are not different from
each other. As we are identical with maya, we cannot know maya. For
this reason, maya is not only unknowable; it is inexplicable as well
Journey from Many to One essentials of Advaita Vedanta by Swami Bhaskarananda