Mukti means liberation, freedom or release from the cycle of rebirth. If achieved while one is still living, it is called jivan mukti. People who accept libration even in jivan mukti (embodied state) subscribe to the view that removal of ignorance is liberation; due to samskaras or vasanas (inborn traits) the body can continue to exist for some more time or till the exhaustion of prarabdha karma (accumulated effects of actions).
The realized self experiences the oneness of Atman or the eternal non-dual bliss here itself, and the fall of the body is referred to as videha mukti (liberation in a non-embodied state). Such people are referred to as ‘siddha-s’ (siddhim gatah). The death of the body is then not seen as the final end.
Upanishads declare that as long as the vital airs do not depart from this body, his prana does not leave. When such a person liberated in bodily existence leaves the material body behind (termed as death in common parlance), the self realizes its cosmic nature; it is never born again in this world of ignorance, conflict and pain. That state is called videha mukti (bodiless freedom).
It has profoundly influence the thinking of ancient sages since the time of the early Upanishads. For instance, it is said in Kena Upanishad (I.2., II.5) that those who achieve self knowledge become eternally free after crossing the world of death.
The state of videha mukti is given various names such as moksha, kaivalya, apavarga and nirvana. In Mundaka Upanishad, it is called ‘merger into the highest of the high.’ It is referred to as supreme Divinity, the mahatma self in Bhagavad Gita II.8.
It is said that just as the rivers merged into the sea, leaving their names and their separate identity, so too, the man of self-knowledge goes into the eternal state, leaving behind the world of name and form. In Bhagavad Gita (II.72), it is called the state of Brahma nirvana or the Brahmi state, which remains eternally undisturbed. At another place, it is called the paramagati (highest state), and Krishna has declared that there is no rebirth when it is reached. It is also called avyaya pada (permanent place) from where there is not return (XV, 5-6).