The shape of the moon appears to change because its position changes during its revolution around Earth. The shape of the moon changes according to the reflection of the sun's light upon its surface.
The moon, which is the second brightest object in the sky, does not actually change its shape as many on earth may observe. The change in appearance is merely a reflection of light from its surface.
When at the new moon phase, the moon is positioned between the sun and Earth. This means its light is not reflected to Earth, but rather the light from the sun bounces from the earth and causes a slight illumination on the moon.
When it moves to the side of the earth during its revolution, a quarter of its side is illuminated by sunlight, making it appear as a crescent shape on Earth. As the moon moves 180 degrees away from the sun, it forms a straight line with Earth, which causes the full moon effect.
All the shapes that are formed by the moon are basically indicators of its position from the sun and earth and how light behaves in relation to each.