Magic is a type of energy that can harness the elemental properties of Vana'diel. People who do so are known as mages. Magic has a varitey of effects that can be brought forth to Protect, Heal, or attack a target with such spells as Stone or Banish.
Some jobs use magic, but are balanced in their melee abilities as well.
And other jobs cast magic-type spells.
Schools of Magic
There are multiple schools of magic: white magic which focuses on healing wounds, black magic which deals damage and performs debilitating status effects on an enemy, and blue magic which is learned from felled enemies. There is also enhancing magic (aka red magic: en~ spells and single target bar~ spells) which primarily utilizes spells that let you enchant your armor and weapons with the elements, and the forbidden summoning magic, which allows one to commune with the avatars and elemental spirits of Vana'diel. Songs, which focuses on using the voice and instruments to enhance allies and enfeeble enemies, and ninjutsu, which uses ninja tools for offensive or stealth-related purposes, are considered "para-magic" or simply talents. There is also brown magic (the "digestive magic") that is only used by some. It uses the same spellcasting animation as black magic, similar to how most monsters that call pets use the summoning magic casting animation.