Once there was a little girl named Bil and her brother, Hjuki (sometimes rendered as Hiuki and sometimes as Hyuki). They were the children of a very cruel man named Vidfinn. Every day, the kids would toil away at their chores, beaten and constantly criticized by their nasty dad.
High in the sky, Mani, the moon god, noticed the plight of these children. Mani was forever being chased around the sky by the monstrous wolf called Hati, and he probably needed a couple of kids around the house to help him out while he was practicing his evasive maneuvers. When that wolf occasionally got hold of the moon, the resulting battle could be seen by humans on earth in the form of an eclipse.
One day, as Hjuki and Bil were heading up a hill to fetch a pail of water, Mani swooped down and took them away to his home in the sky. The kids were doubtless happier there, working for the god of the moon rather than their hateful papa. Thereafter, Hjuki represented the waxing moon and Bil the waning moon—their master, Mani, represented the full moon. No word on whether the kids ever got homesick, however.
In some versions, the kids were heading off to get a bucket of mead from a magical well that flowed with the honey-wine. In another telling, Mani placed a bucket of dew at the top of a hill to lure the children, then snatched them up in his silver chariot and swooped off with them.
Some scholars believe that the familiar children's rhyme Jack and Jill is a folkloric recounting of the story of Hjuki and Bil (see ch'i-lin writeup about that poem for a recounting of a peculiar version of this myth). This theory goes back to an 1866 book called Curious Myths of the Middle Ages, and later authors have elaborated on the story by adding bits with Hjuki and Bil falling down the hill. All of this seems highly speculative to me, but probably makes for a better story.
Much of this information has been gleaned from a (self-published) book on mythology I have written and am constanly in the process of revising.
Monaghan, Patricia "the Book of Goddesses and Heroines (Llewellyn, St. Paul, 1990).
A weird Norse myths-as-fairytales site I found: http://www.geocities.com/Heartland/Lane/8771/moonchariot.html
Goddesses FAQ: http://www.wyrdwords.vispa.com/goddesses/goddessfaq.html#Bil