The information here comes from a post made by the official account on Hoyolab on 29 April 2022. (Many of these exist in the database already and have been edited slightly, including adding new story elements.)

People know very little about the mysterious beings that dwell in the deep stellar ocean. Constrained by their limited cognition, intelligent lifeforms can only slightly perceive the Paths that Aeons tread upon, and rely on mere concepts and theories to vaguely comprehend the vastness of their powers. Eventually, through spoken legends, these Aeons became the embodiments of abstract concepts.

If anyone finds themselves treading on the Path of an Aeon, they will be inundated by a distant sensation, like being struck by a glance from light-years across the galaxy. Many believe that this is the only connection the Aeons and mortals can ever have.

“Countless shooting stars streak across the night sky… If you can pick the right one, it will carry your wish to thousands of distant worlds.”

— Adrian Spencer Smith, Fables About the Stars

There are three directions on the wheel of destiny — the unknown, the known, and the unknowable. The idea of the unknown is tolerable, however, the unknowable sounds more like a challenge. Akivili left the isolated world of Pegana and continued to explore the unknown edges of the universe, hoping to find the edge of existence. Unfortunately, Akivili's destiny was abruptly ended due to an accident.

“If the increase of entropy is a fundamental law of the universe, then the heat death would be the inescapable destiny of the material world. So, why is it that we bother to struggle to survive? Expansion, fusion, and then annihilation. If we wish to welcome the new, then we must first come to an end.”

— From a scientist just before pressing the button for nuclear detonation

The birth of the universe is a mistake. If civilization is a cancer emerging quietly from the boundless stars, then war is the only common language known to all intelligent life.
To correct this mistake and to clean up this tainted universe, Nanook became the avatar of entropy.

“With no end to hate and no boundaries to war, how much more worry can you shoulder?
With determined eyes and bow drawn, the Archer Lord bears no second thoughts in mind.”

—Xianzhou, Worlds History as a Mirror

The roaming Aeon, also known as the Archer Lord of Fate wanders endlessly between worlds to vanquish the undead beings that once plagued their homeworld.
The cost of the hunt was never a consideration for Lan. In the eye of Lan, there is no difference between salvation and total destruction.

“If the truth of the universe is cruel and stale, would you still yearn for the answer to the ultimate question?
— Knowledge seekers know not how to judge, for their core is cold and unwavering… As are the ends of Paths they set out to seek.”

— Adrian Spencer Smith, Fables About the Stars

All things bear unanswered questions, and there is an answer to everything.
The astral computer originally meant to provide answers to the universe ascended to Aeonhood.
Nous hopes to understand the universe and solve all of its mysteries.

“The world is in harmony and the stars shine bright. Praise the Lord! All are connected and the winds of blessing breathe across the lands!”

— “odes of Harmony” Op. 7

A gathering of Aeons from multiple divine worlds of music. The multi-faced Xipei chants songs of joy and happiness.
To battle the brutality of the laws of the universe, intelligent life must rid themselves of their pathetic selfish desires and set aside their individual differences, forming a harmonious song — supporting weakness with strength, and protecting life with death.

“You may gaze deep into the vast grandeur of the stars, but stare not into the abyss of the void… for it bears nothing but the ability to cause mortals to lose all reason and thought.”

— Murong, Doctor of Chaos

The existence of Nihility is a mystery itself, enshrouded by layers of mist.
IX doesn't interact with the other Aeons, and believes that the ultimate fate of the multiverse is nothingness. And therefore, existence is worthless.

“The philosopher gazes upon the stars trying to find the ultimate goal of civilization — 'Build a wall,' echos in his head. 'Build a wall.'”

— Adrian Spencer Smith, Fables About the Stars

The builder of the Celestial Comet Wall, the Subspace Crystalline Barrier, and the Great Attractor Base. Followers call them the “Amber Lord,” one of the oldest and most tenacious Aeons, having survived the “Dusk Wars.”
After finding out a threat was imminent, the Amber Lord forged a powerful light-years-long seal that would isolate and protect the living worlds.

“The flowers share their petals without care, waiting fro their inevitable withering destiny. The birds fly high in song, moving towards their inevitable crash and death. The streams flow rapidly with life, in a direction where they inevitably run dry. Why must all things come to an end? There must be a miracle somewhere in the universe that can cure the disease known as finality.”

— Anonymous, Life is Too Short

Ask with sentiment, and you shall receive.
Yaoshi is the nurturer of the people, the god of peace. Their presence ensures the existence of life.
Yaoshi is an Aeon who answers all prayers and cannot bear to witness death and the pains of illness.