We only see the moon because it reflects sunlight so, if some magical force "turned off" the sun, the moon would disappear from view. Because the moon is a sphere, and because we only see it due to illumination from the sun, its appearance changes as the sun, moon and Earth's relative positions change.
The one phase of the moon that cannot be observed from Earth is the new moon. This occurs when the moon lies almost directly between the Earth and sun, allowing us to see the night time side of the moon -- which is, of course, dark and not visible.
In the days following the new moon, keep an eye on the western horizon just after sunset to spot a very 'young' moon appearing as a slender crescent hanging in the darkening sky. These very young phases of the moon stay close to the sun in the sky so are only visible low in the west as night falls. During the day, the moon appears to follow the sun across the sky.
PHOTOS: Supermoon 2013: Readers' Photos