The moon appears to change shape through the month. These apparent shape changes are called phases. We see these apparent shape changes due to the position of the moon in its orbit compared to the Earth and Sun.

It works something like this:

1/2 of the moon is lit by the sun at all times. (the side facing the sun!)

As the moon moves around the Earth in its orbit we see the moon from a different angle every day.

The phase we see depends upon how much of the lit part of the moon is visible given the angle created by the moon's position in its orbit!

We can only see the side of the moon that faces the Earth. If that happens to be the same side that is facing the sun, we call it a Full Moon! If the opposite side is facing the sun we see nothing, that is the New Moon!

If the lit part is on the right it is said to be waxing. The lit portion appears to be "growing" toward the Full Moon.

If the light part in on the left, it is said to be waning and is approaching the New Moon phase.

A "silly" rhyme seems to help remember which is which:
"If the light is on the right it's waxing. Waxing makes it shinier!"