What is it called hen the lighted portion of them moon appears to get larger?

Waxing.

From the new moon (where it isn't visible) through to the full moon (when it is visible from earth as a full circle, all night long).

At "New Moon" the moon is between the earth and the sun, so we can only see the dark side (but because it's dark you can't actually see it !). Over the next 2 weeks the moon continues it's orbit around the earth, becoming progressively more and more visible as each day goes by, until we see the "full moon", which is when the moon is on the opposite side of the earth to the sun and is fully illuminated by the sun.

Over the following 2 weeks the visible area of the moon reduces, as the moon completes it's monthly orbit of the earth (actually 29.5 days). This is known as waning.