Many people common believe that the phases of the moon are showing the shadow of the Earth on the moon. They believe the sun is shining behind the Earth and the people on the side facing away from the sun are looking at the moon with a shadow of the Earth on it, explaining why the shape of the moon is constantly changing. However, how does that explain a new moon, a full moon, and eclipses? How does that explain waxing and waning gibbous phases?

This misconception seems to have risen from knowledge that the sun is illuminating the moon, but that the Earth stands directly between the moon and the sun.

The phases of the moon can be explained by looking at the position of the moon and where it is relative to the Earth. So it does relate to the Earth's position, but the phases aren't the shadow of the Earth on the moon. Instead, each of the different phases shows where the Moon is in its orbit around the Earth. For example, if the moon is parallel to the sun alongside the Earth, the sun is shining on half the moon, so people looking at the moon will only see half a moon, or the 1st/3rd quarter moon. Similarly, a full moon is where the sun is illuminating on the full moon face. The Earth isn't blocking the sunlight from reaching the moon, so it is being illuminated and we're able to see that.

The below diagram illustrates what we're seeing when we're looking the moon and seeing different phases.