quarter moon

Noun

 * 1)  Either of the intermediate stages between the new and full moons.

Usage notes
In spite of the name, half of the Moon's visible portion is lit up during a quarter moon, hence, it is also called a half-moon. It is called quarter moon because it is at 1/4th or 3/4th of the way of the cycle from one new moon to the next new moon (which is called a “lunar month” or “moon” for short, hence the “quarter moon” designation.)