You're describing the waxing gibbous phase of the moon. Here's why:

* Waxing: This means the illuminated portion of the moon is getting larger as seen from Earth.

* Gibbous: This refers to the shape of the illuminated portion, which is more than half but less than full.

So, a waxing gibbous moon shows a significant portion of its lighted side, but it's not yet a full moon.