Ordinarily, the mid-September harvest moon is no brighter than any other full moon, but it does provide more hours of moonlight.
In autumn, the orbital path of the Moon and its visibility in the sky combine so that it stays above the horizon for an unusually long time at the full moon and a day before and after.
The brightness of the Moon is determined by how much sunlight falls on it, which is pretty much constant; how much appears to be lit up from where we see it, from crescent to full; and how high it is in the sky. The higher the Moon is, the more light we see, because it has a shorter path through the dust and smog of the atmosphere.
In 1997, the harvest moon of September 15 was the brightest of the year, by a small margin, because it came within a few hours of perigee, the Moon’s closest approach to Earth.
The difference in brightness between the Moon’s closest approach and farthest point amounts to 12 to 13 percent. It was also the largest full moon in angular size; its apparent diameter, normally about 30 arc-minutes, was 32 or 33 arc-minutes.
The varying Earth-Moon distance is why solar eclipses are sometimes total, when the Moon completely blocks the Sun, and sometimes annular, with a ring of light visible around the Moon.