There isn't a specific term for when the lighted portion of the moon appears to get larger. However, the process you're describing is called waxing.

* Waxing refers to the period when the illuminated portion of the Moon is increasing in size, from a thin crescent to a full moon.

Here's a breakdown:

* New Moon: The Moon is completely dark and not visible.

* Waxing Crescent: A small sliver of the Moon is visible, becoming larger each night.

* First Quarter: Half of the Moon is illuminated, looking like a quarter.

* Waxing Gibbous: More than half of the Moon is illuminated, becoming fuller each night.

* Full Moon: The entire Moon is illuminated, appearing as a bright disc.

The opposite of waxing is waning, when the illuminated portion of the Moon is decreasing in size, from full moon back to a thin crescent.