As the sun, moon and earth go through their orbits, the sun illuminates the moon at different angles and, as a result, the moon appears to the earth in different shapes, called phases.
New and Full Moon
In both the new and full moon phases, the sun, moon and earth are in approximate alignment. However, during the new moon, the earth is between the earth and sun and the moon's illuminated side is not visible to the earth. During the full moon, the opposite is true; the moon is on the opposite side of the earth, and the entirety of its illuminated side is visible.
Half Moon (First and Third Quarter)
In the first and third quarters of the moon's cycle, the phase is called half moon. During this phase the moon is at a 90-degree angle to the earth and sun, therefore the view from earth is of half the moon's illuminated side and half of its shadowed side.
Waxing and Waning Crescents and Gibbous
The remaining four stages identify the progression of the moon's phases of illumination. Waxing means "growing," waning means "shrinking," and crescent means less than half illuminated and gibbous means more than half illuminated. The waxing crescent phase occurs between the new moon and first quarter, and the waxing gibbous is between the first quarter and full moon. This happens as the moon becomes steadily more illuminated from the earth's perspective. Between the full moon and the end of the cycle, the moon begins to "disappear" again. Therefore, the phase between the full moon and third quarter is called the waning gibbous, and the phase between the third quarter and end of the cycle is called the waning crescent.