Source: http://finalfantasy.wikia.com/wiki/Summoned_Monsters

Also known as "Summoned Monsters", or just "Summons" for short.

Summoned Monsters (幻獣, Genjū?, lit. “Phantom Beast”) are a recurring element in the Final Fantasy series. They are powerful monsters that can be called into battle to fight by their Summoner. The exact nature of summoned monsters varies from game to game, but in some they are depicted as gods or demigods, and their role in the storyline has grown as the series has progressed.

See also"

• Aeon
• Final Fantasy
• Guardian Force