Often described (or translated) as "extinction of the flame", especially in the Theravada tradition.
This is related to the description of the difference between the Hindu and Buddhist understanding of soul (atman and anatman respectively), and hence the difference in their respective understanding of reincarnation.
The Hindu concept is described comparing the atman to a diamond in a crown. When the crown wears out, the diamond is placed in a different crown: The same diamond, different crown, or the same soul (atman) in a different body.
The Buddhist understanding likens reincarnation to a flame of a burning candle. When the candle burns out, a new candle is lit using the flame of the old candle. The flame of the new candle is hence a continuation of the old flame, it is the same and it is not the same. In reincarnation, the non-permanent soul (anatman) provides continuity but not identity of existence (panta rhei).
In nirvana the flame is extinguished. This does not imply anihilation though it denies eternalism, both considered extremes, and thus fallacies, by Buddhism.