Tonight the Moon will look like a “half-moon” but it is officially at the First Quarter. It will be 45 percent visible to us, which certainly sounds like about a half-moon. About half of it will be illuminated by direct sunlight, but it will be only “7 days old” in its waxing growth from the New Moon when its unilluminated side was facing the Earth. So, it is a quarter of the way into its cycle of phases from new to full.
The Waxing (“increasing”) crescent is when the Moon appears to be partly but less than one-half illuminated by direct sunlight.
First Quarter is when it looks like half a circle because it has completed one-quarter of an orbit around the Earth from either the full or new position.
Waxing Gibbous is when it appears to be more than one-half but not fully illuminated by direct sunlight.
The most popular phase, the Full Moon, is when the entire illuminated side is facing the Earth.
And then as we see less of it from Earth, the Waning Gibbous appears to be more than one-half but not fully illuminated by direct sunlight.
The Last Quarter is that other half of the Moon being illuminated by direct sunlight, and the Waning Crescent is the other side of the Waxing Crescent.
A nice site to see all the phases on a calendar is MoonGiant.com