The moon is half dark, half lit on two days each month . What causes this?

This is caused by the rotation and position of the Earth with respect to the sun.

Explanation:

The constant change of the Moon's surface relative to Earth is called "The moon phases".

These modifications in our satellite are due to the change of position of the satellite with respect to the Earth and the Sun.

During the lunar phases of the third quarter and the first quarter, the moon lights up just a half, being that both only light half, the first quarter lights the right side of the moon, and the last quarter lights the left side.