What is the meaning of waxing gibbous phases?

This refers to a phase of the moon where more than half the circle is visible, and occurs just before the full moon where the entire orb is visible.

"Wax" means to grow greater and "wane" means to grow lesser, so the "waxing gibbous" is the 3/4 phase as the moon appears to grow larger, and the "waning gibbous" is the 3/4 phase where the moon appears to grow lessor.

The "new moon" follows the waning gibbous and is, once again, a full orb.

So the sequence is new moon, waxing crescent, first (waxing) quarter, waxing gibbous, full moon, waning gibbous, last (waning) quarter, waning crescent then back again to the new moon.