Magic Points (often abbreviated MP) are a unit of magical power that are used for casting spells. Each spell requires a certain amount of MP to be used in order to cast it. The maximum amount of magic points are determined by the player's race, job, level, and certain gear that is equipped.
Magic points can be replenished by healing; the spell Refresh; the songs Mage's Ballad or Mage's Ballad II; Evoker's Roll; an optional Sanction bonus; certain equipment, medicine or food granting a Refresh Status Effect; or the weapon skills Starlight, Moonlight, Energy Steal, Energy Drain and Spirit Taker. Stepping inside your Mog House or changing Job at a nomad moogle will also replenish your MP.