This year the Harvest Moon falls on October 5th instead of September like last year. It will also occur in September next year.
This is because the Harvest Moon is the full moon closest to the Autumnal Equinox (September 22). The full moon on October 5th falls closer to the official start of fall than the full moon from earlier this month on September 6th.
The Harvest Moon gets its name from folklore. The saying is the light of the moon helped farmers gather crops when days became shorter and nights longer following the Autumnal Equinox.
The difference in the Harvest Moon compared to others is it rises a little later than most full moons. This just means it seems like there are several full moons for a couple nights.
You may have noticed the Harvest Moon appears more orange or red, but the color or size the moon appears does not necessarily change for this particular moon.
A full moon gets its orange/reddish look because of how close it is to the horizon. So when it shortly rises after sunset, it appears to have an orange/red tint.
Each full moon has its own name from folklore and seasonal changes.
Some other common named full moons are the Strawberry Moon in June, Wolf Moon in February and Old Moon in January.