The currency of Adventure High.
You cannot obtain any Gems until you obtain a Crystalizer by visiting the Item Shop for the first time.
Once you do, the Gems you obtain is equal to 10% of the EXP you gain in the Dungeon, including the Mind Dungeons (so 700 EXP gives you 70 Gems, for example).
The Crystalizer obtained is Molly's old one after she finds out how poor the Protagonist is. She explains she can purchase a new one with no problem.