At times when only a narrow crescent of the Moon is seen (e.g. a “new moon"), one can also see the rest of the Moon faintly outlined. The Sun now shines on almost all of the side of the moon turned away from Earth (those calling that “the dark side of the moon" are quite wrong!) and therefore it also illuminates most of the side of the Earth facing the moon. If you were standing on the moon at that time, a “full Earth" would shine brightly in your sky, and the faint “earthshine" of the darker part of the moon is just the reflection of some of that bright earthlight.
Earthshine is of interest to scientists, because its brightness is contributed by all the factors which turn back sunlight before it manages to heat the Earth--light reflected from the ground and from clouds, and light scattered back by dust and small particles (“aerosols") in the atmosphere. In a time when atmospheric scientists are trying to assess heating of the Earth by the greenhouse effect (http://www.phy6.org/stargaze/Sun1lite.htm), earthshine measures a process which works in the opposite direction, reducing the heat our planet receives.
The fraction of light reflected is hard to estimate theoretically, but earthshine allows it to be measured. According to recent reports (“The Darkening Earth,” Scientific American August 2004, p. 16), this fraction has been growing, reducing the amount of sunlight received by Earth and canceling about 1/3 of the greenhouse heating.