Damnation is the equivalent of "hell", the concept of everlasting divine punishment and/or disgrace, especially the punishment for sin as threatened by God.
In Vorin theology's version, during the Desolations the Voidbringers came again and again, trying to force mankind off Roshar and into Damnation. Just as they once forced mankind and the Heralds out of the Tranquiline Halls, the equivalent of "paradise". It was described as the place where the Voidbringers were forged from hatred. Damnation likely refers to the place where the Heralds spend time between Desolations, a place of eternal fires and torture. This explains why the Herald Talenel appears so exhausted when he returns to Roshar at the end of The Way of Kings.
"Damnation" is used throughout the book by all characters, as a swear or curse, such as "Storming Damnation", "There's no way in Damnation" or "Damnation's own fool!".
The concept of Damnation is likely shared by other people as well, as it was mentioned by Szeth despite his being from Shinovar. He believes that his murders and sins would damn his soul to continued existence of agony and punishment.
|“||The flesh burning. The fires. The pain over and over...||”|
|“||Lost, Tvlakv? Perhaps you should pray to the Almighty for guidance. I hear he has a fondness for slavers. Keeps a special room in Damnation just for you.||”|
|“||Ten heartbeats ... Return to me, you creation of Damnation.||”|