Nibbana (Pali, from Sanskrit nirvana) is a Buddhist term, which definition is different from the Hindu term nirvana.
While some Buddhist interpret nibbana in a similar manner as Hindus, that is, “dying out” or “extinction” (as of a fire), others find in it an archaic meaning of “he who is cooled,) such as cooled from the fever of greed, hatred, and delusion, the three principle evils of Buddhist thought. The Buddha explicitly denied the Western interpretation of the term as complete extinction or annihilation.
However, while nibbana does not mean extinction, neither does it mean that after death the individual exists in some manner or other. When the body ceases to function, the phenomenal personality disappears.
Buddhism denies the existence of a soul at any time, whether before or after death. An early Buddhist brother wrote, “Illusion has utterly passed from me. Now I am cool, all fire within gone out.” A third-century, BC, Indian text states that nibbana “is really only the inner realization of the stored impressions”
Nibbana is a state that can be realized in the here and now as well as after death. In the third century BC, the Milindapanha states that the Buddha still exists but “has passed completely away in nibbana, so nothing is left which could lead to the formation of another being. And so he cannot be pointed out as being here or there.”
Later in the same work, probably in a different hand, the nibbana is described as “the City of Righteousness.” Here the liberated man “enters the glorious city of Nibbana, stainless and undefiled, pure and white, unaging, deathless, secure and calm and happy, and his mind is emancipated as a perfect being.” A.G.H.
Rice, Edward, Eastern Definitions: A Short Encyclopedia of Religions of the Orient, Garden City, New York, Doubleday, 1978, pp. 275-277