What causes the moon to have different appearances (crescent, full, etc)?”
We can only see the part of the Moon that faces the Earth, and that the Sun shines on. The Sun shines on only half of the Moon, which may be all, part, or none of the part of the Moon that is facing us. The Moon revolves around the Earth so that this angle is constantly increasing or decreasing, with the Moon at the middle of the angle. As the angle changes, the light and shadow on the Moon appears to change from our perspective. The link below gives a good pictorial demonstration of this. I hope this helps.
