The moon festival is celebrated on the 15 day of the 8 month of the lunar calander. This one one of the three biggest holidays in Taiwan aside from Chinese New Year and Dragon Boat Festival.
The moon festival is a fun time where families get together have a BBQ and celebrate being together (much like a western Thanksgiving)
There are many various tales of the moon and the moon festival. The one I am most familiar with is the story of Hou-Yi and Chang’e, who drank an immortality potion and floated up toward the moon. You can read the whole Moon Festival Story here.
Aside from BBQ Taiwanese also eat moon cakes. The moon cakes range from sickening sweet to savory. They are round to symbolize the shape of the full moon which means a full family.
There is a unique tradition around moon festival when pomelo fruits are fresh, people clean out the fruit and wear the rind on their head as a hat. This is suppose to freshen your mind.