Mid-Autumn Festival

The Mid-Autumn Festival (Chinese: 中秋節 / 中秋节), also known as the Moon Festival or Mooncake Festival, is a traditional festival celebrated in Chinese culture. Similar holidays are celebrated in Japan (Tsukimi), Korea (Chuseok), Vietnam (Tết Trung Thu), and other countries in East and Southeast Asia.
It is one of the most important holidays in Chinese culture; its popularity is on par with that of Chinese New Year. The history of the Mid-Autumn Festival dates back over 3,000 years.
 The festival is held on the 15th day of the 8th month of the Chinese lunisolar calendar with a full moon at night, corresponding to mid-September to early October of the Gregorian calendar.
 On this day, the Chinese believe that the Moon is at its brightest and fullest size, coinciding with harvest time in the middle of autumn. 
Lanterns of all size and shapes, are carried and displayed – symbolic beacons that light people's path to prosperity and good fortune. 
Mooncakes, a rich pastry typically filled with sweet-bean, egg yolk, meat or lotus-seed paste, are traditionally eaten during this festival.
 The Mid-Autumn Festival is based on the legend of Chang'e, the Moon goddess in Chinese mythology.

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 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.

•    Thanksgiving, to give thanks for the harvest, or for harmonious unions
•    Praying (asking for conceptual or material satisfaction), such as for babies, a spouse, beauty, longevity, or for a good future

Moon worship

Chang'e, the Moon Goddess of Immortality

Houyi helplessly looking at his wife Chang'e flying off to the Moon after she drank the elixir.
An important part of the festival celebration is Moon worship. The ancient Chinese believed in rejuvenation being associated with the Moon and water, and connected this concept to the menstruation of women, calling it "monthly water.
 The Zhuang people, for example, have an ancient fable saying the Sun and Moon are a couple and the stars are their children, and when the Moon is pregnant, it becomes round, and then becomes crescent after giving birth to a child. These beliefs made it popular among women to worship and give offerings to the Moon on this evening.
 In some areas of China, there are still customs in which "men do not worship the moon and the women do not offer sacrifices to the kitchen gods.
In China, the Mid-Autumn festival symbolizes the family reunion and on this day, all families will appreciate the Moon in the evening, because it is the 15th day of the eighth month of the Chinese lunisolar calendar, when the moon is at its fullest. There is a beautiful myth about the Mid-Autumn festival that is Chang'e flying to the Moon.
Offerings are also made to a more well-known lunar deity, Chang'e, known as the Moon Goddess of Immortality. The myths associated with Chang'e explain the origin of Moon worship during this day. One version of the story is as follows, as described in Lihui Yang's Handbook of Chinese Mythology.
In the ancient past, there was a hero named Hou Yi who was excellent at archery. 

His wife was Chang'e. One year, the ten suns rose in the sky together, causing great disaster to the people. Yi shot down nine of the suns and left only one to provide light. An immortal admired Yi and sent him the elixir of immortality. 

Yi did not want to leave Chang'e and be immortal without her, so he let Chang'e keep the elixir. However, Peng Meng, one of his apprentices, knew this secret. So, on the fifteenth of August in the Chinese lunisolar calendar, when Yi went hunting, Peng Meng broke into Yi's house and forced Chang'e to give the elixir to him. Chang'e refused to do so. Instead, she swallowed it and flew into the sky. Since she loved her husband and hoped to live nearby, she chose the moon for her residence. When Yi came back and learned what had happened, he felt so sad that he displayed the fruits and cakes Chang'e liked in the yard and gave sacrifices to his wife. People soon learned about these activities, and since they also were sympathetic to Chang'e they participated in these sacrifices with Yi.
When people learned of this story, they burnt incense on a long altar and prayed to Chang'e, now the goddess of the Moon, for luck and safety. The custom of praying to the Moon on Mid-Autumn Day has been handed down for thousands of years since that time.
Handbook of Chinese Mythology also describes an alternate common version of the myth.
After the hero Houyi shot down nine of the ten suns, he was pronounced king by the thankful people. However, he soon became a conceited and tyrannical ruler. In order to live long without death, he asked for the elixir from Xiwangmu. 
But his wife, Chang'e, stole it on the fifteenth of August because she did not want the cruel king to live long and hurt more people. She took the magic potion to prevent her husband from becoming immortal. 

Houyi was so angry when discovered that Chang'e took the elixir, he shot at his wife as she flew toward the moon, though he missed. Chang'e fled to the moon and became the spirit of the moon. Houyi died soon because he was overcome with great anger. Thereafter, people offer a sacrifice to Chang'e on every fifteenth day of eighth month to commemorate Chang'e's action.

https://en.wikipedia.org/wiki/Mid-Autumn_Festival