Gazing at the Moon on Festival moon cakes is an ancient tradition from the Zhou Dynasty (around 500 BC) when people held ceremonies to welcome the full moon, with huge outdoor feasts of moon cakes, watermelons, apricots, apples, grapes and other fresh fruits. The popularity of this ancient tradition began to grow during the Tang and Song Dynasties when people of high rank held banquets in their big courtyards. They drank fine wine, watched the moon and listened to music. Common people who could not afforded as big parties as the rich would lay some food such as moon cakes and fruits on a table in the courtyard and pray to the moon for a good harvest. This underwent a great rise during the Song Dynasty, and historical documents tells about mid-autumn night in the capital, where people would stream to the night markets and together with their families admire the beauty of the full moon. There are also many classic songs and well-known verses about this tradition.

2. Eating Mooncake

Eating moon cakes while watching the full moon is a central part of the mid autumn festival throughout China, and is a symbol of family unity. At the very beginning, the moon cakes were served as a sacrifice to the Moon. The words moon cake first appeared in the Southern Song Dynasty, even though, at that time, the moon cakes were not round. Nowadays, moon cakes are given as presents to loved ones and it represent people’s wishes to be together during the mid-autumn festival.

Apart from these two traditional customs, different regions have their own celebrations.
Source : http://www.chinatravel.com/facts/chinese-festivals/traditional-chinese-festival/Middle-Autumn-Festival.htm#1

I. Chang’e Flying to the Moon
It is said that long ago there used to be 10 suns in the sky. Each day, one of the suns would travel around the sky on a carriage driven by Xihe, the mother of the suns. One day, unexpectedly, all 10 suns simultaneously appeared in the sky, which instantly dried the crops and caused disaster to the people on earth.
Hou Yi, a local archer, had great sympathy for people’s sufferings from the blistering weather and decided to help them out. Houyi climbed up to the summit of Kunlun Mountains and shot down the suns leaving only one to benefit people. After he shot down the sun, Hou Yi became a hero who was revered by local people.

Later, Hou Yi married a beautiful girl—Chang’e. The young couple lived a happy and sweet life.

Hou Yi was so famous for his perfect archery skills that he had a lot of apprentices, including the unrighteous Peng Meng. One day when Hou Yi was on the way to visit his friend, the Queen Mother of the West gave him an elixir of immortality as a reward for his heroic undertaking. Meanwhile, he warned Hou Yi “Do not swallow this pill before preparing yourself with prayer and fasting for a year”.  Hou Yi gave the elixir to Chang’e for safekeeping and she took it as a treasure and hid it in her jewelry box. Unfortunately, Peng Meng found this secret and made a plan to steal it. Several days later, when Hou Yi and other apprentices went out for hunting, Peng pretended to fall ill and stayed at home. After they left, Peng forced Chang’e to give him the elixir. Chang’e, knowing that she could not defeat Peng, swallowed the elixir herself, and mmediately she felt herself floating up and flied to the sky. With deep love to her husband, Chang’e chose to be an immortal on the moon, closest to the earth; then she could see her husband every day.

In late afternoon, Hou Yi came back and was told what had happened. Heart-stricken, Hou Yi went to the back garden and called his wife’s name ceaselessly. Surprisingly, he found that the moon was extremely clean and bright that night; and that there was a moving figure like Chang’e in the moon. Hou Yi desperately tried to catch up with the moon, but he could not do it. Hou Yi then asked servants to set a table in his back garden and with his wife’s favorite snacks and fruits on it. In a short time, more and more people heard about the news that Chang’e had become an immortal, and they also put tables under the moon to pray to Chang’e for good fortune and safety. From then on, the custom of worshipping the moon on the Mid-Autumn Festival began to spread in China.

II. Jade Rabbit Making Heavenly Medicine
This legend is considered to be an extension of Chang’e Flying to the Moon. It tells about three sages who transformed themselves into pitiful old men. One day they met a fox, a monkey and a rabbit, and they begged for food. The fox and the monkey shared their food with the old men; but the rabbit, with nothing to share, jumped into a blazing fire to offer his own flesh instead. The sages were so touched by the rabbit’s kindness that they sent it to live in the Moon Palace, where it became the Jade Rabbit. Chang’e, who lived alone after arriving in the moon, liked the Jade Rabbit at the first sight, and therefore kept it company. As the time went by, Chang’e and Jade Rabbit became inseparable friends. Hearing about the story of Chang’e and Hou Yi, the Jade Rabbit felt sympathetic to them and decided to make a special heavenly medicine, which could help Chang’e return to Earth. Unfortunately, the Jade Rabbit has still not been able to make it even though he has worked hard for thousands of years. Observing the moon on the Mid-Autumn Day carefully, we can still see the Jade Rabbit making his heavenly medicine.

III. Wu Gang Chopping the Cherry Bay
There is also another story about the Mid-Autumn Festival. Many years ago, Wu Gang, an immortal in Heaven, was punished to chop down the cherry bay in the moon for his serious mistakes. The cherry bay in the moon was extremely luxuriant and sturdy with a height of 5167 meters. It would also heal up as soon as it was chopped, which made Wu Gang’s work last for thousands of years.

The mid autumn festival has many traditions and activities in which people express how much their families mean to them, and how much they miss absent members.

Source : http://www.chinatravel.com/facts/chinese-festivals/traditional-chinese-festival/Middle-Autumn-Festival.htm#1