When this last story was told to me as a child, it included Luna, Celestia's supposed sister. Permit me to tell it that way as well; the versions that do not include Luna are mostly similar in any case.
Before the sun was tamed, she was the lost deity of ponykind.
After the death of Northern Bound, the name "Celestia" slipped bit by bit from the memories of those who knew Northern Bound. No other pony but her had spoken to Celestia, after all, and she had never been the most involved of spirits. Her only legacy was the sun and moon and the spell to raise and lower them. So in time, she became nothing more than the sun again, an image in the sky that the unicorns bandied about however they wished. Ponykind simply continued their old beliefs, nevermind the truth that had once been known about the sun.
Did Celestia care? It's hard to say. On one hoof, she had Luna with her to keep her company. And she certainly seemed content to let her name pass into obscurity. One can only imagine what might have happened had she, say, stoked the flames of a cult in her image. Instead, she allowed herself to be nothing more than the sun.
But on the other hoof, she must have kept that light deep in her heart. As a partially tamed creature, she had become tied inexorably to ponykind; she could no more pretend otherwise than to pretend that she was not the sun. To taste something good, and then to know that it is available at any moment, is a constant temptation. And Luna! Sweet Luna. As the new goddess of the moon, she deserved to achieve the same bond with ponykind that Celestia had once established. So surely Celestia must have wanted to maintain and strengthen her connection with ponykind, even though she did not. The reasons why she chose to bide her time are unknown. Ask her yourself, and see if she will answer.
As to the reason why she returned when she did, that is obvious. The ponies began to bicker, and their home grew covered in snow and ice, and she feared that if she did not act, she would lose them forever.
This story is well-known to any colt or filly having lived more than one winter. But O listener, imagine yourself in those days, when you did not know what was going to occur, and consider how you might have felt, believing that it might have been the end of days. In that moment, Celestia recalled her love of ponykind, and she began to appear in dreams, begging those she visited to overcome their prejudice and live in harmony. (My mother always said that this, the ability to appear in dreams, was a sure sign that Luna had existed. But I retain some doubt; for if Luna could walk in dreams, surely Celestia could as well. But for the sake of the story, I will set my skepticism aside for the present.) Most ponies, one would think, upon meeting an ancient sun goddess would surely change their behavior to avoid catastrophe. But the ponies in that time were nothing if not bull-headed; if anything, their hatred grew even worse. Celestia despaired, because she saw the ponies she loved dying again before her very eyes.
And then the magic of friendship saved them, and Celestia realized she had so much more to learn.
She had known friendship, but briefly. She had her sister. But she needed to join ponykind in the full beauty of connectedness, which she could not do as she was. She discussed it with her sister, who agreed. It was time for them to be gods no longer.
They searched for many years for the perfect family; there were many good stallions and mares they could have chosen. But in the end, they found Star Swirl the Bearded and his wife, Lady Astra, who was past the age of motherhood but had not borne any children. The two introduced themselves and explained their desires. In order to learn the magic of friendship, they needed to become ponies, just like any other. They wanted to be born, grow up as fillies, discover their talents, and become capable, dependable mares. They thought that this might be a hard sell, but to their shock, Star Swirl and Astra accepted through teary eyes. That morning, when they woke up, Astra found herself with child. After a single day and a single night, she went into labor, and through a quick, painless birth came twins into this world--Celestia first, then Luna.
Here the stories diverge one last time. In some of the stories, the princess or princesses are born alicorns; in others, they are born unicorns, and they only earn their wings once they have discovered their talents. In some of the stories, they are immediately crowned princesses; in others, Star Swirl hides them from the world until much later; in still others, they live perfectly ordinary lives as fillies. In any case, we know how all the stories end. The nation rallies behind Celestia, Luna disappears (a story for another time), and the world is safe under one thousand years of peace.
And in this way, the sun was tamed for good.