The illuminated part of the Moon appears to change shape because of the relative positions of the Earth, Moon, and Sun. As the Moon orbits the Earth, the angle at which sunlight strikes the Moon changes, causing different parts of the Moon to be illuminated.

When the Moon is between the Earth and the Sun (during a new moon), the side of the Moon facing Earth is not illuminated, so we cannot see it. As the Moon moves around the Earth, more of the side facing Earth becomes illuminated, until we reach a full moon, when the entire side facing Earth is illuminated.

The exact shape of the illuminated part of the Moon depends on the precise angles between the Earth, Moon, and Sun. These angles change over time, so the shape of the illuminated Moon appears to change as well.