The Forsaken Altar is a mechanic that only appears in prestige games. It offers "stormforged cornerstones", which are typically supercharged variants of legendary cornerstones, for a price of citadel resources and settler lives.
As a point of comparison, the legendary cornerstone Survivor Bonding offers +1 global resolve and +10% villager speed, while the stormforged variant by the same name offers +3 global resolve and +25% villager speed.
The Altar can only be activated during Storm season, and allows you to peruse the available perks before choosing and paying. You can choose which citadel resources and which settler races you wish to pay with. You can choose to forego paying with blood, but this increases the cost in citadel resources. Food Stockpiles, Machinery, and Artifacts are worth 1, 2, and 3 points apiece respectively.
The Altar also requires you to have made a certain amount of progress on the settlement; activations become available after 3, 6, and 9 points of Reputation earned. If a stormforged cornerstone has not been claimed, the altar activation point remains available.
The choices available to you persist from storm to storm.