What are Earth Gemstones for?
Earth gemstones can be used as a magic crafting catalyst to create quad-cast spells with one additional cast per stone used. This is fairly useful for magic casting builds or needs.
As Shawn points out, it is also used in a Cid side quest to upgrade the Valiant machine weapon.
They're used to upgrade a weapon, specifically the Valiant.
However they're also good for making spells, causing "intense" damage and range.