It takes approximately 27.3 days for the Moon to orbit the Earth. This is known as the sidereal period. However, the time it takes for the Moon to complete a full cycle of phases (from new moon to new moon) is about 29.5 days. This is called the synodic period.

The difference between these two periods is due to the Earth's simultaneous orbit around the Sun. During the time the Moon completes one orbit around the Earth, the Earth has moved a significant distance along its orbit around the Sun, thus requiring the Moon to travel a little farther to reach the same phase.

Source: Space.com