Avatar, Daemon, Genius, Eidolon, Spirit Guide, Soul. All terms used to refer to that eternal part of mortals: what continues on after death. But what is this avatar? A Technocrat will tell you that it is a figment of the unconscious genius that leads the bearer to conscious innovations. A Shaman will tell you that it is a spirit companion that gives insight into the workings of the world. A Hermetic will tell you that it is a guardian angel or demon that offers up excellence in return for devotion to its cause. Some of them equate it with soul, others say they are separate, while some deny the soul altogether.
Consider the following essay to be out of game knowledge of one way that it could work, which the storyteller has fitted together from the myriad sources of World of Darkness cosmology to attempt to make a unified whole. It will not synch entirely, but it comes a sight better than many theories. Feel free to have your character believe anything, but use this essay as a guideline for how it could all fit in the world you'll be playing in.
The Chorus will tell you that the beginning of being was when the One splintered into the Wyck who splintered into all the avatars of creation. The Dreamspeakers will tell you that the dreams of Gaia created the myriad spirits that made the world more than a ball of mud. The Euthanatos will tell you that souls are wiped clean of transgressions on the transition from death to life. The Cult of Isis will tell you that souls go to Duat or A'aru on their death, only coming back at Osiris' need. It all comes down to the basis of the game: Belief.
The Primal Marks flaw tells us that your avatar can be a god or totem spirit. The Manifest Avatar merit tells us that your avatar can form itself outside and hold a conversation. The Phylactery flaw indicates that an avatar can become tied to a person, place, thing, or idea. All of this and more seems to indicate an avatar separate from the mage, an entity that grants power through seekings, choosing to grant or deny excellence to the mage.
Yet what sense would that make? Why are there thousands of awakened mages running around and so few of them are granted the power needed to fulfill their avatar's agenda. Why are there references to werewolves sharing the avatar of Gaia and vampires sharing the avatar of Caine? The Technocrats, for once, are closer to the truth.
The awakened avatar is part of the mage's own soul, the part that can conceive of altering reality and grant insight to the mage to perfect himself. Much like the Shadow of a wraith, the Avatar is part of the mage's spirit that is separate but not independent. Also like the Shadow, most Avatars pretend to have more power than they really have. Yet the avatar is just the soul, and the awakened avatar just happens to have multiple personalities. Some mages interact with their avatars the same way an unawakened individual deals with the subconscious, but others like to have a mentor figure, someone to answer questions and show the path. And take the blame. A seeking, regardless, is the way a mage's unconscious shows the conscious mind how to achieve further wisdom when it is time to try for it. A mage fails not because he has failed to please his avatar, but because he has subconsciously realized his own inability to progress.
So what is the avatar or soul? It is finite but part of the infinite. It can be neither created nor destroyed, but it can be altered, divided, fused, grown, shrunk, or reformatted. In short, it is a piece of spirit-stuff that resonates with its own particular harmony, and everything about it can change except the fact that is does exist. Whether this spirit stuff broke from the One or from Gaia's dreams, there are a few important things about it.
Avatars can be gods or greater spirits. While undoubtedly many of those with Primal Marks of Hercules are suffering from low self esteem on a spiritual level, at least some of those with an avatar that claims to be a god have to be telling the truth. Even the ones that claim the same god. It's pretty simple - a mortal can become a god and a god can become a mortal. Look at the definition of the word Avatar. Like I said, it's about belief. If enough people believe in a mortal's divinity he can become divine. Look at Isis and Thoth, Apollo and Athena, Odin and Thor. Any one of these legendary beings could have been a mortal that amassed enough power and worship to transcend the mortal body. On dying these mortal souls become spirits of great power, and feed on worship, perhaps even destroying the mortal body in a fire of purification as the spirit sings forth.
So why would a mortal who'd achieved godhood, or a god that'd always been divine, choose to return to mortal form? Any number of reasons, in fact. By being a spirit, one is fed by belief and exists only on the prayers of the masses. Some greater spirits, like Gaia and the Triat, have enough sway to draw power directly from the tellurian and feed it to the spirits that serve them. Some greater gods have enough worship to fuel servitors that are not part of an acknowledged pantheon. The number of worshippers on the planet are few, compared to the number of spirits, and those that feed themselves from the prayers of sleepers are always looking to oust a competing god. And so gods will become beaten, splintered, and weakened by others, or simple inability to promote a church. There is an option of taking on mortal form once more. Mortal bodies are part of the world and draw power by existing, and are, also, a great way to hide from enemies. An avatar in mortal form is unable to ascend easily to the powers it would possess in spirit form, but it is not in danger of fading into nothingness with lack of belief.
The soul parts of Mummy show how an avatar can be invested in a Phylactery or manifest outside the mage. Part of the soul is simply capable of being outside of the mage and connected by the Khu across the gulf of space. A Phylacteried mage has part of the soul with an affinity for some noun, the part that allows the use of magic. Similarly, a manifest avatar has some portion of its spiritual ability to manifest remaining.
Garou are their avatars - half spirit, half flesh, bound in the service of Gaia. Vampires are the victims of the blood avatar of their origin, having their original soul shredded and rebound by the Khu of whatever was their progenitor in the chain of the blood. Wraiths are nothing but avatars, having lost the path to incarnation and become pure spirit but forced to feed off of emotion rather than worship. Changelings are fae avatars fused to mortal hosts to become something more. Mummies are avatars bound together and tied to a mortal khat by the power of the spell of life and Osiris' godhood. Each are awakened in their own way, possessing their own powers, but mages are those most interested in the process.
Every mage has a fragment of what was once, or could become, a god, and the power to make this fact evident.