Why the Moon changes shape

The Moon makes no light of its own. Half of it is always lit by the Sun, and half is always dark. What changes through the month is how much of the lit half we can see from here.

When the Moon is roughly between us and the Sun, its lit side faces away — that is the new moon. A week later we see half of the lit side. When the Moon is on the far side of us from the Sun, we see the whole lit face: a full moon.

It is not the Earth's shadow that makes the phases. The Earth's shadow only falls on the Moon during an eclipse, which is much rarer.