An item sometimes found when a character kills an enemy with the status effect Signet, Sanction, or Sigil on.
There is one kind of crystal for every element.
Crystals can be used for the Synthesis of new items. Additionally, crystals can be traded to any NPC who offers Signet in return for Rank Points, which is sometimes needed to receive the next mission.
There are 8 kinds of crystals, with each element corresponding to a different crafting "task", and each can be found at the Auction House under the category "Crystals":
Fire Crystal - Burning or Heating
Earth Crystal - Bonding
Water Crystal - Diluting, Dissolving, or Liquifying
Wind Crystal - Carving or Cutting
Ice Crystal - Freezing or Congealing
Lightning Crystal - Disintegrating or De-synthesizing
Light Crystal - Mending, Repairing, or Blessing
Dark Crystal - Decaying or Aging