It's called the "opposition effect" and is similar to a phenomenon called "dry heiligenschein" here on Earth: you can see the latter when you look out of the window of a low-flying aeroplane, and see a bright patch on the ground surrounding the shadow of the plane. Lunar astronauts observed this same bright patch surrounding their shadows as they walked around on the moon. For instance, if you take a look at the famous
Buzz Aldrin photo from Apollo 11 (2.4MB jpg), and zoom in on the reflection in his faceplate, you can see a bright halo of heiligenschein around the reflected shadow of his head. That's the same view Aldrin would have had when he looked at his own shadow.
When we look at the moon from Earth, it has a small enough angular diameter that the
whole moon shows the same apparently anomalous brightening when it is "down sun" from us: that is, at full phase.
Grant
