The Crystal, as it is called in-game, is a guaranteed reward from the Abyssal Sire. It drops in quantities from 1-5.
The Crystals are used to upgrade all three dream sets to their tier 1, tier 2, and tier three variants which have 1.5x, 2x, 2.5x their original stats respectively. These upgrades render the sets untradeable, lest you spend 200M DSCoins to revert the upgrade.
The upgrade to T1 takes 250 Crystals, T2 from T1 takes 500 Crystals (750 cumulative), and T3 from T2 takes 750 crystals (1500 cumulative).