This is caused by earthshine. This is similar to the light that the moon provides for us when it is full. Just as a full moon reflects the sun's light onto our surface, the reflection of the sun's light from the earth's surface illuminates the moon in the same way. Of course, the directly sunlit part of the moon (the crescent) would appear much brighter than the earth lit part. So next time you are out early in the morning or evening and you see the crescent moon, look closely to see if you can spot the rest of the moon's disk, illuminated faintly by earthshine.