Available after completing the quest I Can Hear a Rainbow, these heretic mages have unlocked the secrets of the forbidden magic of Vana'diel by creating a pact with the Avatar known as Carbuncle. Through his suggestion, these mages have the choice to delve further into the craft and create pacts with up to 12 more of the Avatars of Vana'diel after defeating them in battle to prove their worth. If accepted, Summoners are able to fight alongside them in order to bring peace to Vana'diel.
Avatars can be obtained through quests by obtaining the appropriate elemental tuning forks. Elemental Spirits can be obtained either through merchants, or by defeating certain monsters that drop the scrolls (these scrolls can also be bought on the Auction House). Each Avatar/Elemental Spirit has an inital MP cost as well as a perpetual MP cost that is based on the SMN's level.
For more information, please see Summoner Avatar Costs.