If I may take the perspective of a wannabe evoloutionary biologist for a moment, there is a perfectly reasonable explanation for this which should be obvious to you if you've ever been out during a full moon far away from city lights. You'll find that it's very easy to see at night when the moon is full or near-full, as long as there are no other sources of bright, ambient light to compete.FanofDeath said:Whether it be mental or a spiritual thing, people seem to draw energy from that certain phase of the moon. I, myself, get a bit of a boost off of a new moon. It's not an uncommon thing, though, so don't worry about insanity.
Now, before the development of fire or flex-time, the main thing limiting our activity at night would have been that we were simply unable to see well when it got dark. That limitation goes away when the moon is full; you can easily see well enough to get around. I think I remember some studies showing that light levels can be correlated to activity levels in humans, and implicated nocturnal light sources (such as the lights in your house) as a potential contributor to insomnia.
Now, as to the specific effect of the full moon on early humans I can only speculate. It may be a heightened alertness/edginess to be on the watch for nocturnal predators, or just an urge to party all night long and get some 10,000 BC action (could be that, at the time, lunar cycles and women's cycles just about matched up).