Here's an image that describes the phenomenon I'm asking about. The very thin sliver to the left is of course the surface of the moon as lighted by the sun. But the rest of the moon is also faintly lighted -- by what?
I'm guessing that some amount of "earthshine" -- sunlight reflected from the earth -- is the culprit here, but I've found no authoritative confirmation online. It would be great to have a link to a source that explains what's really going on.