What causes the cyclical changes in the appearance of the moon?

The changes in the phases of the Moon are caused by its position towards the Sun, not as it is commonly thought that it is because of the Earth's shadow on it.

What we see from the Moon, the bright part and the almost invisible dark part (looking with bear eyes of course), is only dependent on how the Moon is positioned towards the Sun. The part that is bright is the part that faces the Sun, while the part that is dark is the part that is on the opposite side, thus not facing the Sun.

Depending on the Moon's position towards the Earth as well, we can sometimes see it as partially bright, as half bright, full bright, and everything in between, and that depends on how the Moon is positioned towards the Earth.