When the Moon is a thin crescent we can often see a phenomenon known as the "the old moon in the new moon's arms" or "the new moon in the old moon's arms". The image above shows the first of these: inside the waxing crescent is the ghostly image of the full moon.
Leonardo da Vinci was the first to explain what was happening. He realised that the Earth and Moon are both being illuminated by the Sun from essentially the same angle. So, for example, the side of the Earth facing a full moon is entirely in darkness. Conversely, the side of the Earth facing a thin crescent Moon is almost entirely in sunlight. Just as the full moon shines brightly on a dark Earth, so a sunlit Earth shines on a dark Moon, only even more brightly, as the Earth is larger and more reflective. It is this Earthshine that we are seeing, lighting up the portion of the Moon which the Sun cannot reach.
Slight overexposure of the sunlit portion of the Moon makes the crescent seem larger that it really was.
Image: © T. Credner, AlltheSky.com.