It is not annihilation but rather the extinguishing of the three fires of greed, hatred, and delusion. When these are eliminated, what remains is a state beyond conceptual understanding - neither existence nor non-existence as we ordinarily conceive them.
The Buddha himself remained largely silent about the precise nature of nirvana, suggesting it must be experienced rather than described. It represents complete freedom from attachment, the end of craving, and the realization of ultimate truth. Various Buddhist traditions have developed different understandings of nirvana, but all agree it represents the highest spiritual attainment.
Source
Buddhist Sutras