When one observes the phases of the moon he is simply observing the moon's day and night, a natural shadow from the sun illuminating half of the moon at any one time.
The moon moves in a slow circular pattern around the hub of the earth similar to the sun. Therefore the shadow on the moon will change slightly from day to day, as the angle of the moon differs. At first quarter moon the celestial moon is hung overhead of the observer. This will illuminate approximately one half of the moon's surface; when the observer looks up he will see a shadow cutting the moon in half. As the moon moves westward, it becomes located at an angle to the observer whereas its phases will slowly modify, changing to a waxing gibbous.