One possible explanation that comes to mind is that the dark part we see on the Moon is the shadow that the Earth casts on it. But there are problems with this explanation. For one, if this were true, the Moon should be in its new phase when it at its farther from the Sun. We know when this happens, because then the Moon rises at the same time as the Sun sets; and we can observe that at this point the Moon is full, not new! Besides, if the Moon passes through the Earth's shadow every month, then when it is at the opposite side of its orbit it should get directly in between the Sun and the Earth, producing a solar eclipse much more often than it actually happens. No, this explanation cannot be the right one.

Why does the Moon have phases, then? The Moon does not emit light on its own; all the moonlight we see is actually light coming from the sun that is reflected on the moon surface. The part of the Moon that is illuminated is the half that is facing the Sun. But from here, the Earth, we cannot always see that same half; instead, we see only the half facing us. The parts of the Moon that are on both halfs (the illuminated one, and the half facing Earth) are the parts that we can actually see from here.

Position of the Moon in orbit (left) and its corresponding phase (right) (The Sun is initially in the upper-left direction)

• When the Moon is roughly in the same direction as the Sun, its illuminated half is facing away from the Earth, and therefore the part that faces us is all dark: we have the new moon. When in this phase, the Moon and the Sun rise and set at about the same time.
• As the Moon moves around the Earth, we get to see more and more of the illuminated half, and we say the Moon is waxing. At first we get a sliver of it, which grows as days go by. This phase is called the crescent moon.
• A week after the new moon, when the Moon has completed about a quarter of its turn around the Earth, we can see half of the illuminated part; that is, a quarter of the Moon. This is the first quarter phase.
• During the next week, we keep seeing more and more of the illuminated part of the Moon, and it is now called waxing gibbous (gibbous means "humped").
• Two weeks after the new moon, the moon is now halfway through its revolution, and now the illuminated half coincides with the one facing the Earth, so that we can see a full disk: we have a full moon. As mentioned above, at this time the Moon rises at the time the Sun sets, and it sets when the Sun rises. If the Moon happens to align exactly with the Earth and Sun, then we get a lunar eclipse.
• From now on, until it becomes new again, the illuminated part of the Moon that we can see decreases, and we say it's waning. The first week after full, it is called waning gibbous.
• Three weeks after new, we again can see half of the illuminated part. This is usually called last quarter.
• Finally, during the fourth week, the Moon is reduced to a thin sliver from us, sometimes called waning crescent. A while after four weeks (29.5 days, more precisely) the illuminated half of the Moon again faces away from us, and we come back to the beginning of the cycle: a new moon.

Now, if all planets revolve around the sun, shouldn't other planets also present phases? The answer is yes, and the fact that Venus has different phases was one of the arguments in favor of putting the Sun in the center of the Solar System, and not the Earth (as it was believed before). The phases of Venus are similar to those of the Moon, only that to complete a cycle we have to wait until the relative positions of Venus and the Earth repeat. This takes much longer than for the Moon: it's about 20 months.