Understanding the "between" lunar phase names is easy if you break out and define 4 words: crescent, gibbous, waxing, and waning. The word crescent refers to the phases where the moon is less than half illuminated. The word gibbous refers to phases where the moon is more than half illuminated. Waxing essentially means "growing" or expanding in illumination, and waning means "shrinking" or decreasing in illumination.
The Third quarter moon is when the moon is at its halfway point on the "waning" cycle. After this pase, it will recede more and more until it becomes a New moon.