What is the waxing and waning of the moon?

Waxing is when the moons illumination gets bigger.

Waning is when the moons illumination gets smaller.

As the moon orbits the earth, what you see from earth, is the moon reflecting sunlight. This changes from day to day. Starting with a thin sliver, it gets larger (Waxes) until it is a full moon.

Then it gets smaller (wanes) until it goes to a sliver again and then not visible (new moon).

This cycle repeats over 28 days.