What happens astronomically
As the Moon moves along its orbit, its angular separation from the Sun increases and a larger share of the illuminated hemisphere becomes visible from Earth.
Moon phases
Waxing Moon
The Moon is called waxing after New Moon and before Full Moon, while the illuminated fraction of its visible disk is increasing.
What you can see from Earth
It begins as a thin evening crescent, reaches First Quarter and then becomes waxing gibbous.