Vikshepa is known as a projection in Hindu philosophy. It
refers to that aspect of an illusion where the non-real is superimposed on the
real. The Advaitins argue that it is avidya which is responsible for avarana
(concealment) of the real, and vikshepa (projection) of what is illusory
appearing as real.
Maya in Advaita Vedanta signifies the illusion of the
multiplicity of the empirical universe, when the Brahman is the only Reality.
Maya in Rig Veda means supernatural power and in
Shvetashvatara Upanishad it signifies cosmic illusion.
Adi Shankaracharya has accepted maya, avidya, adhyasa, and
vivarta as synonymous terms and makes a distinction between two aspects of maya
– avarana and vikshepa.
The avarana, veil, being negative, conceals the real nature
of the Brahman, while vikshepa, being positive, projects the world of
multiplicity over the Brahman. It conceals the real and projects the unreal.
When the Brahman is perceived through the veil of maya, it appears as God, man
and this world (Ishwara, jiva and prapancha).
Avidya considered as individual nescience, is illustrated by
the rope-snake analogy and, as cosmic nescience, the Brahman is projected as the
empirical world of names and forms. The Brahman appears as the worlds, even as
the rope appears as the snake.
Maya is the finalizing process belonging to the Brahman and
has the two properties of avarana or hiding the truth and vikshepa or misrepresenting
it (Tajjayatve sati, tajjanayajanako vyaparah). We do not perceive the
Absolute, but we apprehend something else in its place. So avarana is the
earlier stage of vikshepa in terms of a tempral series, though they are
inseparably blended in the cosmic force (maya) of the Brahman.
Source – Encyclopedia of Hinduism Volume XI page 352 - IHRF