I prefer Discworld's explanation:
The moon is slightly closer to the Disc than the sun, and is covered, on one half, with silvery glowing plants, which feed the lunar dragons[1]. The other half is burnt black by the sun. The moon rotates, and completes a full revolution in about a month; the full moon occurs when the luminescent side is completely visible from the Disc, the new moon when the dark side is shown. The sun's orbit is so complex that one of the elephants has to cock its leg to allow the sun to continue on its orbit.