The cyan crystal is a quest item used in the Mourning's Ends Part II quest. It is obtained by solving the first part of the light puzzle in the Temple of Light, found upon searching the chest in the blue room. It is needed in order to progress further through the puzzle.
Interestingly, whenever you attempt to alchemise the crystal with any alchemy spell, elven magic forbids it and a message will appear saying "You can't do that to elven crystal!".
Upon finishing the quest, the cyan crystal is the only remaining piece of the puzzle left in the player's inventory.
Furthermore, trying to bank it will result in the message: "A magical force prevents you from banking this item.", so it is recommended to destroy it, as it has no further use.
You can leave it in a pillar before completing the quest, certainly it is not possible afterwards, attempting to gives the message "The Temple of Light's safeguards are working fine for now, so I'd best not meddle with them." Destroying it gives the message "Resetting the light maze will generate a new crystal".