"Here where the souls of the wicked are tortured in the pits of Tartarus, the wailing and agony of the damned, resonated deep throughout the bowels of the Underworld." - Gaia
In Greek mythology, Tartarus is the darkest depths of the Underworld. It is where the souls of the evil are sent to for eternal torture, and its where Zeus imprisoned the Titans. In some variations of the myths, Tartarus is also a Titan being like Gaia. He made love to Gaia as well, having Gaia birth Typhon as a result.
In God of War: Chains of Olympus
In God of War: Chains of Olympus, Kratos was defeated by Charon the ferryman, and subsequently thrown into the prisons of Tartarus. As he attempted to make his way out of the depths, Kratos fought his way through hordes of enemies, came across the prison of the Titans, and obtained the Gauntlet of Zeus, which aided his escape.
In God of War III
In order to craft a special weapon for the Spartan warrior, Hephaestus told Kratos to retrieve him the Omphalos Stone. The stone, however, was said to dwell deep within the Pits of Tartarus, deep below Hephaestus' forge. Kratos first needed to solve the puzzle of the door that lead to the Pits of Tartarus, then battled his way through its darkest depths, until ultimately coming face-to-face with Cronos the mighty Titan. After a vicious battle, Kratos slew Cronos and retrieved the Omphalos Stone.