Chest loot from the chest that appears after completing each region of the Domain of Anguish. The number of gemstones rewarded is equal to the number of regions completed without leaving the Domain of Anguish (2 per region in Hard Mode); the type of gemstone depends on the region, e.g. Stygian Gemstones in the Stygian Veil.
Historical note: Anguish Gemstones used to be required to unlock the hero Razah, but this requirement was removed in the April 5, 2007, game update. Characters who had already unlocked Razah before this update could get the gemstones refunded through the quest Money Back Guarantee.