As the moon orbits around the Earth, we see it from different angles. These different viewpoints, catching the light and dark portions of the moon (as lit by the Sun) from varying perspectives, are what causes the moon to appear to change shape. It takes the moon approximately 28 days to complete a full rotation around the Earth. During this time it appears to take on different shapes, known as phases. There are four principle phases that occur during each cycle.
When the lighted side of the moon faces away from the Earth, the moon visible in the night sky looks very dark. This phase occurs when the Sun, moon and Earth are aligned in an almost perfectly straight line with the moon positioned between the Earth and Sun.
During the first quarter phase, the right side of the moon is lighted and the left side is dark. In the time period between the new moon and the first quarter moon, the lighted portion of the moon appears progressively larger until an entire half of the moon is lit. This is responsible for the characteristic crescent shape of the moon.
When the entire lighted side of the moon faces the Earth, we see a full moon. Just as in the new moon phase, the Sun, moon and Earth are all aligned in an almost straight line. However, during this phase the Earth is between the Sun and moon, allowing us to see the entire lighted side of the moon.
This phase is also known as the third quarter. In this phase, the left half of the moon appears lighted while the right side of the moon appears dark. During the time between the full moon and the last quarter moon, the part of the moon that appears lighted shrinks every day.