The Wikipedia has a decent write up. I think of this as Chuseok, the Korean harvest moon festival, but the other Sino-centric cultures have their own versions of the Chinese festival.

中秋节 / Mid Autumn Festival

The festival is so-named as it is held around the autumn equinox on the 15th of the 8th lunisolar month in the Chinese calendar.[5] Its name varies among Sinitic languages, with the most common one being Mid-Autumn Festival or simply Mid-Autumn (中秋), as well as its traditional calendar date, either Fifteenth of the Eighth Month or Half of the Eighth Month, which is more regional. Other regional names include Eighth Month Festival, used in places such as Northeast China, Southern Fujian, and Jianghuai; Festival of Unity (simplified Chinese: 团圆节; traditional Chinese: 團圓節; Wugniu: doe2-yoe2-ciq7; Nanjingese: tuang2 üän2 zie5), used in Shanghai and Nanjing; and Mooncake Festival (simplified Chinese: 月饼节; traditional Chinese: 月餅節; Jyutping: jyut6 beng2 zit3), used in Guangdong and Hong Kong.[14] Outside of Greater China area, there are several other names for the festival:

Chuseok (추석; 秋夕; lit. ''autumn eve''), Korean festival celebrated on the same day in the Chinese and other East Asian lunisolar calendars.[15]
Tsukimi (月見; lit. 'moon viewing'), Japanese variant of the Mid-Autumn Festival celebrated on the same day in the Chinese lunisolar calendar.
Moon Festival or Harvest Moon Festival, because of the celebration's association with the full moon on this night, as well as the traditions of Moon worship and Moon viewing.
Tết Trung Thu (節中秋 in Chữ Nôm), in Vietnam.
Also known as The Children's Festival in Vietnam. Most festival songs are sung by the children.[16]
Lantern Festival, a term sometimes used in Singapore, Malaysia and Indonesia,[17] which is not to be confused with the Lantern Festival in China that occurs on the 15th day of the first month of the Chinese calendar.
However, 'Mid-Autumn Festival' is more widely used by locals when referring to the festival in English and 'Zhōngqiū Jié' is used when referring to the festival in Chinese. [citation needed]
Bon Om Touk, or The Water and Moon Festival in Cambodian. The festival is held each year in November for 3 days.[18]
Meanings
The festival celebrates three fundamental concepts that are closely connected:

Gathering: Such as family and friends coming together, or harvesting crops for the festival. It is said that the Moon is the brightest and roundest on this day which means family reunion. Consequently, this is the main reason why the festival is thought to be important.
Giving thanks: To give thanks for the harvest, or for harmonious unions through activities like giving mooncakes to each other.
Praying (asking for conceptual or material satisfaction): Praying for things such as babies, a spouse, beauty, longevity, or a good future.
Traditions and myths surrounding the festival are formed around these concepts,[19] although traditions have changed over time due to changes in technology, science, economy, culture, and religion.[19]

Origins and development
The Chinese have celebrated the harvest during the autumn full moon since the Shang dynasty (c. 1600–1046 BCE).[19][20] The term mid-autumn (中秋) first appeared in Rites of Zhou, a written collection of rituals of the Western Zhou dynasty (1046–771 BCE).[1] As for the royal court, it was dedicated to the goddess Taiyin Xingjun. This is still true for Taoism and Chinese folk religion.[21][22]...