This holiday is always celebrated on 10 October and is the national holiday of Taiwan.
It marks the start of the Wuchang Uprising of 10 October 1911.
The revolt marked the end of the Ching (Qing) Dynasty that had been established in 1644 by the Manchus. The revolt led to the founding of the Republic of China on 1 January 1912.
The Double Ten Day is celebrated in Taiwan as a national holiday. Double Ten is observed on October 10 every year. It is the celebration of the start of the Wuchang Uprising which later led to the Xinhai Revolution.
Wuchang uprising marks the start of the end of the Chinese dynasties. Unhappy with the Manchu controlled Qing dynasty, revolutionaries in China were gathering to overthrow the Qing dynaster. Amongst these revolutionaries was Dr. Sun Yet-Sen, who helped found the Tongmenghui (同盟會.) Sun Yet-Sen spent much of his time overseas trying to get funding for the uprising. This was also because Sun was exiled from China since a previous Guangzhou uprising (1895.)
The end of the Qing Dynasty was finalized with the last emperor Puyi abdicating his throne on Feb 12, 1912.