Why does the moon look different at different times of the month?
The apparent phases of the Moon aren't really the result of any physical change in the Moon itself, but are caused by changes in the relative positions of the Earth, Sun, and Moon. The light we see on or from the Moon is actually a reflection of light from the Sun. Because the Moon orbits around the Earth on a regular, predictable pattern, we experience a twenty-nine day cycle of Moon phases. The darkness we perceive as being part of these phases is really a shadow.
At the New Moon, the Moon is directly between the Earth and the Sun. In this position, no light reaches the side of the Moon that we can see. At night, it may appear that there is no Moon at all because of this shadowed position. Throughout the month, the Moon enters into a waxing phase. This means that the Moon is slowly moving out of position between the Earth and the Sun, and more light is reflecting off of it. To us, it may look as though the Moon is growing little by little every night. When the Moon is at a ninety-degree angle to the Earth and Sun, we see a half-lit Moon. As it continues in its procession around the Earth, it will come to a full Moon, where the surface we see is entirely reflecting the light of the Sun. Slowly, the Moon continues to move back into shadow. Then the cycle repeats all over again!
Some cultures base their calendars on this regular waxing and waning of the Moon--this is called a lunar calendar.