Earthshine is a soft, faint glow on the shadowed part of the moon caused by the reflection of sunlight from the Earth. Specifically, Earthshine happens when the light from the sun is reflected from the Earth's surface, to the moon, and then back to our eyes. Because of this double reflection of light, Earthshine is many, many times dimmer than the direct light of the sun on the moon. Earthshine is even more faint because the moon's "albedo" (a specific kind of reflectivity) is less than Earth's. Even though this dim light is only a reflection it can still illuminate some features of the moon.
Moons orbiting other planets can also experience this phenomenon, generally called "planetshine".
Leonardo Da Vinci explained the phenomenon nearly 500 years ago. He realized that both Earth and the Moon reflect sunlight. But when the Sun sets anywhere on the Earth-facing side of the Moon (this happens every 29.5 Earth-days) the landscape remains lit -- illuminated by sunlight reflected from our own planet. Astronomers call it Earthshine. It's also known as the Moon's "ashen glow" or "the old Moon in the New Moon's arms."
