The Lunar Cycle
There are eight phases in the lunar cycle. It starts with the new moon, followed by the waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter and waning crescent. The lunar cycle then repeats.
The Sun Reflected
The moon rotates around the Earth, which is why the lunar phases change. We are able to see the phases of the moon, such as the first quarter, because the sunlight reflects off the surface and back at us. As the moon rotates, more or less of the moon is visible to us depending on where the moon is in relation to the Earth and sun. If the Earth is directly between the sun and the moon, sunlight illuminates the entire surface, and the result is a full moon.
The First Quarter
During the first quarter phase, the moon is located beside the Earth in relation to the sun. That is, the core of the moon and the Earth are roughly an equal distance from the sun. This position causes the moon to appear half illuminated by the sun's light. In the northern hemisphere, the right half of the moon is illuminated. In the southern hemisphere, the left half is illuminated.
Last Quarter Moon
The first and last quarters are easily confused because the moon appears almost identical to everyone on Earth. The difference is that the moon is on the other side of the Earth, and the opposite side is illuminated by the light from the sun. In the northern hemisphere, the left side of the moon is visible, and in the southern hemisphere the right side of the moon is visible.