The Moon takes 27.3 days to orbit Earth but 29.5 days to get back to the same phase.

By the time it has completed one lap against the background stars, Earth has moved a month's worth along its own orbit, so the Moon has to travel a little farther to line up with the Sun again. The first number is the sidereal month, the second is the synodic month, and calendars are built on the second one.