Shine On
The full moon closest to the autumnal equinox is called the Harvest moon. There are several reasons why. The reason that is almost too obvious to mention (but I will), is that this is a peak harvest time of the year. Throughout history, farmers could continue harvesting well into the night.
Also, just as the sun rises directly east and sets directly west on the first day of Fall, so does the moonrise and moonset around this time of the year. This puts the moon pretty much directly overhead in the night sky, rather than lower in the sky, which makes the lighting a little bit brighter than usual.