Avatars are the celestial and terrestrial powers capable of being called forth by summoners.
Avatars as Allies
Avatars can form pacts which allow adventurers to summon weaker versions of themselves. These "summoned avatars" are only a portion of the avatar's true strength. Avatars are capable of using powerful abilities: normal physical attack and Blood Pact abilities--both physical and magical--that require the summoner's MP to use. To maintain the avatar's presence, an Avatar Perpetuation Cost is constantly required.
Avatars as Enemies
Certain beastmen (such as Yagudo or Lamiae) have summoners within their ranks. Certain beastman summoners are capable of summoning the exact same avatars that summoners of the playable races can and have access to most of their abilities. Most avatars summoned by beastmen will have generic names similar to the elementals summoned by other beastman summoners.
There are currently a total of nine avatars that are available to summoners.
There are eight known celestial avatars from the Windurstian Vana'diel Stellar Map, however till now, only six of the basic element avatars appeared in the game.
From the map (take note of the names that are in all caps), we can see the celestial avatar of light is Alexander and the celestial avatar of darkness is Odin.
The term "celestial avatar" is a player-given name due to the fact that they are referred to as "celestial beings" and from the fact that they are opposite of the terrestrial avatars. In-game they are usually referred to as the sleeping gods. They are also more godly than their terrestrial counterparts.
Each one has a story involving the past of the celestial avatars when they were regular creatures.
There exists two beings for each protocrystal avatar: one that is one of the original gods, and the other is a living being (as seen in the avatar legends). During the Meltdown, the energy of the protocrystals (or some other sources of elemental energy that the Zilart extracted from the five mothercrystals) was simultaneously released. Over the centuries, that energy accumulated inside the bodies of the living beings on this planet, causing them to crystallize. Thus they took the form of the protocrystals with the celestial avatars residing. The avatars' souls are probably that of the gods where their body is that of the lifeforces they "merged" with.
The sleeping gods call each other "the true gods" whereas they call the terrestrial avatars "the false gods" and look down on all who came after them.
The sleeping gods are currently in a slumber. When energy is sapped from them (such as by obtaining the "whisper" or "eye" key items), they are closer to awakening. When they awaken, they will try to restore Vana'diel to its original state (known as "paradise") which would only allow for Zilart and gods to live freely (and reduce the terrestrial avatars to mere beasts). It would also allow for the resurrection and death of Promathia, which would bring about the end of Vana'diel.
The sleeping gods also desire to restore the power of the "divided god" which is presumably the key to restoring paradise. The god is, more likely than not, Promathia, as a part of him is found in every lifeforce. Another, less likely possibility is Alexander, or it could just be their name for the true mothercrystal (before it was split (divided) into five parts by Altana in an effort to keep Promathia alive).
The Zilart also used the power of the sleeping gods to help heal Vana'diel after the war between the wyrms and the Zilart.
The great ancient who it is said will fight against Odin in the age of judgement.
The terrestrial avatars are five powerful gods born of Vana'diel to protect the five mothercrystals. They, like any beast, can die, and if Vana'diel was restored to its original state of paradise, they would be reduced to simple animals.
A gigantic wolf summoned by Karaha-Baruha during the Great War, whose power was unleashed in a last-ditch effort to drive back the Shadow Lord's armies from the gates of Windurst. Fenrir aids the summoner with his command over darkness and abilities related to phases of the moon.