Zenkai is the Saiyan ability to grow much stronger after surviving a near-death experience. Zenkai is inherently genetic, and can only be utilized by those with Saiyan blood.

In the Namek and Frieza sagas, it is an important element, but is abandoned after the Frieza Saga, except for when Cell returns from his self-destruction on the North Kai's planet stronger than before.

For expample, when Vegeta recovers from his fight with Goku, his pwer level went from 18,000 to 24,000. It is also implied by Vegeta during the frieza saga that it only applies to elite class fighters.

From Dragon Ball Wiki, a Wikia wiki.