The story
Hòu Yì shot down nine of the ten suns that were burning the earth and was given the elixir of immortality for it. His wife Cháng'é drank it — to keep it from a thief, in the kind telling — and rose to the moon, where she has been since with a jade rabbit that pounds medicine.
He set out her favourite food every year on this night and looked up, and that is the festival: not a story about the moon so much as one about looking at it from a distance and knowing someone else is.
The moon on this night is reckoned the roundest of the year, and round is the same word as reunion, which is the whole festival in one pun.