Soulstones are powerful crystals taken from inside slain Demon Beasts. They store power relative to the strength of their original host and are commonly used for spells and to power magical tools in the Continental Nations. They have different shapes and colors depending on strength and element (the darker the more powerful), but seem to have standard designs based on which beast they have been harvested from.
Along with Flaming Water, Soulstones are one of the major exported resources of the Red Desert, and the hunting of Demon Beasts for the stones has become an important part of the Desert Tribes' infrastructure - particularly in order to trade to the continents for iron.
Like the beasts they come from, soulstones are ranked on a letter scale with the highest known being SSS.