Despite sharing the name in the English localization of Final Fantasy XIV, the abilities known as Stone III in the title are in fact the recurring Stonega spell in Japanese.
Stone III is a tier 3 Black Magic spell. An upgraded version of the Stone II spell, it deals Earth-based elemental damage to a single target. Stone III is the first of the third tier elemental spells available for the jobs that can use it. It serves as a preferred method of inflicting earth damage to single targets during the level 50 - 70 leveling period for the pure casting jobs that have access to the spell.