A trigger(トリガーtorigā), as the name implies, is something that initiates or triggers a magic (or a spell). Four types of triggers are recognised in Magical Girl Lyrical Nanoha/A's Visual Fan Book.
A long incantation, usually required for complex magic or powerful spells. Arias often include a mage's personal incantation, such as Nanoha Takamachi's "Lyrical! Magical!" Reinforce, and later Hayate Yagami, require arias for most of their spells even when less powerful mages do not.
A short command phrase, also known as trigger code(トリガーコードtorigā kōdo). For example, Fate Testarossa's command phrase for her shooting skills is "Fire!" In cases where a mage does not need an incantation to activate a skill, the Device may bark the command in its master's stead.
Action trigger (アクショントリガーAkushon torigā)
A motion, usually a distinctive swing of the Device, or a finger snap. Action triggers usually accompany command phrases.