The phases of the moon are caused by the earth's rotation, the moon's orbit around the earth, and also depends on the earth's position relative to the sun and the moon (since the sun is the source of the moon's light).
There are different phases of the moon: new moon (all dark), waxing crescent (a growing crescent), waxing gibbous (a growing gibbous, which means about half of the moon can be seen), full moon, waning gibbous (shrinking gibbous), waning crescent (shrinking crescent), and new moon.
Half of the moon is always lit up by the sun, unless the sun is eclipsed by the earth.