Why does the Moon change shape during the month?

The Moon seems to change shape because sunlight reaches only one side of it, and Earth sees that sunlit side from changing directions as the Moon orbits us. The Moon itself stays whole; our view shifts from dark, to crescent, to half, to full, and back again.

A lovely detail is that the thin crescent and the round full Moon are both made by the same steady sunlight. Nothing is being sliced away. The Moon is simply moving around Earth, so the bright part we can see grows and shrinks across the month.