There is a story of the origin of this festival, it is said that in a plan to overthrow the Mongols, messages were stuffed into mooncakes (Kanom Wai Pra Jan ขนมไหว้พระจันทร์ 月餅 ) and handed out to the villagers like an ancient form of 'Twitter or Facebook'! The message spread and the people helped to overthrow the Mongols in what would be the beginning of the Ming Dynasty.
However history reports that the festival derives from a Harvest Festival known as Zhōngqiū Jié (中秋節, 中秋节) going back 3000 years to the moon worship of the Shang Dynasty.
For more information take a look at Wikipedia in English and also in Thai
The local people come to the festival which lasts three days, enjoy shopping for moon cakes and other food, enjoy the concert, lion dances and street market. A ceremony is held to pay respect to the King by lighting candles and singing the National Anthem followed by a prayer ceremony to pay respect to the Moon.
Moon cakes are made here in Phuket by the traditional cake shop - Kengtin as well as other bakeries around Thailand, and are usually on sale for about one month before the festival. Local people will buy the mooncakes as gifts for their family, friends and business associates. Originally introduced to Thailand by Chinese immigrants, the cakes are usually filled with red bean, lotus seed, and over the years various new fillings have been developed such as durian, pineapple, chestnut, and apple and cranberry. You can see how the cakes are made in Kengtin's photo album on facebook.
On the same day as the moon festival is the birthday of Yue Lao 月老诞 the 'Old Man in the Moon' an important figure in Chinese marriage.
On the day after the Moon Festival is the birthday of Sun Wukong 孫悟空 known in English as the Monkey God in Thai as เห้งเจีย one of the most well know of Chinese Gods.