The renewal was an event in Horta culture when once every 50,000 years the Horta died out to make way for the next generation of their race.
The event was thought by Federation scientists in the 24th century to be a form of population control; Horta were extremely long lived, had no natural predators and were near indestructible. So to make way for a new generation the Horta laid eggs in the Vault of Tomorrow and then all but a single caretaker, the Prime Mother, died so that their young could hatch into a new uncrowded world.
The Hortas only chose the best of their generation to be the Prime Mother, resulting in their species being remarkably civilized and intelligent. (TOS novel: The Rise and Fall of Khan Noonien Singh, Volume 1)
The Horta underwent a renewal in the 23rd century which was almost disastrously interrupted when the Federation established a mining colony on their homeworld and unknowingly destroyed thousands of eggs in the Vault of Tomorrow. Fortunately an understanding of the Horta was reached between the two parties before all the eggs were lost. (TOS episode & novelization: The Devil in the Dark)