Gauntlet Gems are earned from Caches at the end of each Sector in Gauntlet Mode. They are used to make purchases from the Gauntlet Store. Tap Redeem from the Gauntlet menu to access the Gauntlet Store. 

At the Gauntlet Store, you can purchase Hero Fragments, XP, Gear, and Gear Fragments. The available items refresh after a certain amount of time. You're also able to instantly refresh the list of available items by paying a  small sum of gold. Note that the prize list will update from time to time, and some items may be removed or replaced periodically.