The moon appears to wax and wane through different phases due to how much of its illuminated surface is visible from Earth. At any given time, half the moon is illuminated by the sun's light. Depending on where the moon is in relation to the Earth, the amount of illuminated surface changes. The ratio of illuminated surface to shadowed surface creates the phases.
When the moon is between the Earth and the sun, its illuminated side faces away from the planet. This is a new moon, when the visible surface is completely dark. As the moon travels through its orbit, the illuminated surface slowly becomes visible, waxing into first a crescent moon and then a half moon. After the half-moon comes a gibbous moon, in which three-quarters of the illuminated surface is visible. Finally, when the moon is directly opposite the sun, it becomes a full moon with its illuminated face entirely visible.
The moon's phase also determines when it becomes visible in the sky. A new moon is in the sky at the same time as the sun, and therefore is not visible with the naked eye. As the moon waxes, it begins to rise later in the day, until the full moon rises at sunset and sets at sunrise. The waning moon continues this pattern, rising later and later, until the new moon rises with the sun once again.