The relative positions of the Sun, Earth, and Moon give rise to the phases of the Moon. As the Moon orbits the Earth, it reflects sunlight back to Earth. The amount of sunlight that is reflected depends on the angle between the Sun, Earth, and Moon.
When the Sun, Earth, and Moon are at a right angle, or 90 degrees apart, we see a quarter Moon. This phase occurs twice each month, once before the full Moon and once after. During the first quarter Moon, the right half of the Moon is lit by the Sun. During the last quarter Moon, the left half of the Moon is lit by the Sun.
The other phases of the Moon are also caused by the changing angles between the Sun, Earth, and Moon. The full Moon occurs when the Moon is opposite the Sun in the sky. The new Moon occurs when the Moon is between the Earth and the Sun.