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The Moon revolves around the Earth about once a month. During this period, the Moon rotates around its axis exactly one time. The lunar month, which lasts 29 1/2 days, served as the basis for early calendars. But the Jewish and Moslem calendars are still based on the lunar month. The Moslems attribute such importance to the Moon that some Moslem theologians were quite upset when man walked on it for the first time. Because the Moon both revolves around the Earth and rotates around its own axis during the same period, the same side of the Moon always faces the Earth. To prove this to yourself, try walking around a room while facing an object in its center. You have obviously made on revolution around the object. At the same time your eyes, while focused on the center, have passed over all four walls of the room as you made on rotation around your own axis. You have made one rotation and one revolution and the object in the center has always been facing your eyes, never the back of your head.
Since one side of the Moon continually faces the Earth, people tend to think of the other side as the "dark side of the Moon". This is a misnomer. Just because we do not see it, does not make it dark. Of course, if a tree falling in a forest with no people around makes no sound, then does the Sun shining on the far side of the Moon light it up? But I digress.
A lunar phase is one of the shapes of the lighted portion of the Moon as seen from the Earth. During the course of every lunar month, the Moon passes through all its phases, from the invisible new Moon, to a tiny sliver, gradually to a circular full Moon and then back to a sliver and invisibility. The phases of the Moon are caused by the rotation of the Moon around its axis. As the Moon rotates, the Sun's rays continually light up a different half of it.
Let us follow the Moon during one lunar month. First we see a new Moon. During a new Moon, the Sun directly faces the far side of the Moon. The far side of the Moon is completely lit up, while our side is totally dark. After a few days, the Moon has revolved around a bit. The rays from the Sun have begun to reach the side of the Moon facing the Earth. Because the Moon is a sphere, the line between the dark and light on the moon's surface, called the terminator, appears curved. The lighted section of the near side of the Moon now appears as a crescent. Sometime the dark portion of the near side is not completely black, but a dark blue. The Moon cannot directly produce any light and the Sun is not directly shining on this portion of the Moon. The dark portion is being slightly lilt up by rays of light that have traveled from the Sun to the Earth and then have bounced off from the Earth to the Moon. This phenomenon is known as "earthshine" or the "old Moon in the new Moon's arms".
When the Moon has revolved exactly one quarter of a revolution, its phase is known as the "first quarter". During the first quarter, the near side of the Moon has a bright half and darkened half. The Sun's rays are now reaching the Moon at a right angle to a line drawn between the Earth and the Moon.
Another few days, over half of the near side of the Moon is lit. The dark portion of the near side of the Moon is now crescent shaped and the phase is known as a gibbous Moon. Finally the entire near side of the Moon is lit up. The Sun, the Earth and the Moon now are more or less on a straight line. The Moon is once again gibbous after a few more days pass by, but now the bright portion of the Moon appears on the left side, instead of the right.
When the Moon has revolved three-quarters of a revolution from the time of its new Moon phase, as you might expect, the last quarter has been reached. Once again, exactly half of the near side of the Moon is lit up. During the next quarter the lit portion grows smaller and smaller until once again there is a totally dark new Moon.
Another way of thinking about the phases is to imagine the terminator, the line between dark and light, creeping across the Moon. During the new Moon the terminator is on the right edge of the Moon. The edges of the Moon as seen from Earth are called its limbs. Very slowly the terminator moves across the entire face of the Moon, until the entire near side of the Moon is lit and the full phase has been reached. Now the terminator once again starts to move from the right limb of the Moon, this time spreading darkness, until the entire face has been darkened and the new Moon phase has been reached.
The terminator points to the most interesting part of the Moon for observations. What gives certain areas of the Moon such a dramatic appearance are not only the geographical features themselves, but also the shadows they create. Ironically, a full Moon is not nearly as interesting as a crescent of gibbous Moon. During a full Moon, the Sun is shining from high above the lunar valleys and mountains. There are almost no shadows and it is difficult to spot small features. Even small features of the Moon are prominent at the terminator.