“Moonspinners. They’re naiads – you know, water-nymphs. Sometimes, when you’re deep in countryside, you meet three girls, walking along the hill tracks in the dusk, spinning. They each have a spindle, and onto these they are spinning their wool, milk-white, like moonlight. In fact, it is the moonlight, the moon itself, which is why they don’t carry distaff. They’re not Fates, or anything terrible; they don’t affect the lives of men; all they have to do is to see that the world gets its hours of darkness, and they do this spinning the moon down out of the sky. Night after night, you can see the moon getting less and less, the ball of light waning, while it grows on the spindles of the maidens. Then, at length, the moon is gone, and the world has darkness, and rest, and the creatures of the hillsides are safe from the hunter and the tides are still…
Then, on the darkest night, the maidens take their spindles down to the sea, to wash their wool. And the wool slips from the spindles, into the water, and unravels in long ripples of light from the shore to the horizon, and there is the moon again, rising from the sea, just a thin curved thread, reappearing in the sky. Only when all the wool is washed, and wound again into a white ball in the sky, can the moonspinners start their work once more, to make the night safe for hunted things… ”
from The Moonspinners, by Mary Stewart

When Nicola, (a young Englishwoman on vocation on Crete) tells this legend to wounded Mark (an Englishman also vacationing there), she does so to sooth them both. Mark is feverish, but cannot seek a medical help in a nearby village without risking being found by the bad guys who shot him when he inadvertently witnessed a murder.
I’ve not encountered this legend before, and I couldn’t find whether it’s a part of Greek mythology, a folktale or a story invented by Mary Stewart. Anyway, I like both the “explanation” for the Moon phases and the peaceful, fanciful tone of the legend. For those who prefer an explanation without Naiades, here is a more scientific explanation (an excerpt from text by The University of Texas McDonald Observatory):

“The Moon has phases because it orbits Earth, which causes the portion we see illuminated to change. The Moon takes 27.3 days to orbit Earth, but the lunar phase cycle (from new Moon to new Moon) is 29.5 days. The Moon spends the extra 2.2 days “catching up” because Earth travels about 45 million miles around the Sun during the time the Moon completes one orbit around Earth.”

Image from NASA, via space.com
Image on top from www.mirror.co.uk