The boundary between the illuminated part of the Moon's disc and the dark part is called the terminator. At the time of the quarter moon, it is essentially a straight line running north-south. At other times it will appear as a curved line.
The circular edge of the disc itself is called the limb, and the points where the limb and terminator join (roughly at the lunar poles) are the cusps.
There are usually two parts to the limb - the illuminated portion is called the bright limb, whilst the less obvious portion which is not in sunlight is called the dark limb.
Photo: Morio Higashida.