The "harvest moon" is considered to be the full moon that falls closest to the first day of autumn. This year, the full moon that occurs Saturday is the closest to the September 22 autumn equinox, so the title of "harvest moon" goes to this Saturday's full moon.
When the moon is full, it rises around sunset in the east and is in the sky all night long. It then sets at sunrise. The harvest moon is rather special because the moon's path across the sky from sunset to sunrise appears to travel close to the horizon. This results in the moon rising less than a half-hour from one night to the next. A more common difference is some 50 minutes.
For years, farmers took advantage of the light of the harvest moon after the sun had set. It allowed them to work into the night gathering their harvest. In Europe, where the name "harvest moon" originated, the moon often rises as little as 10 minutes later each night.