Sun Yat-sen influenced China by helping to cause the overthrow of the Ch'ing (also known as Manchu) Dynasty. By doing so, Sun ushered in an era in which various factions fought for control of China. This eventually led to the victory of the communists. Sun is revered by both the People's Republic of China (mainland China) and the Republic of China (Taiwan) as the main force in creating modern China.
Before Sun, China was ruled by the Manchus whose hold on power was weakening; China was helpless against Western countries that forced concessions from it. It was also unable to stand up against Japan in the Sino-Japanese War of 1894. These things helped convince Sun and others that revolution was needed to fix China's problems.
In 1911, Sun's revolution overthrew the Ch'ing and China entered a new era. This is the main influence Sun had on China.
I'd like to add something to the answer provided by pohnpei397 that I think is very important in discussion Sun Yat Sen's influence on modern China; The Three Principals of the People.
This is a political philosophy that Sun created as a plan for making China a powerful nation. It is claimed as a basis for the political ideologies of Mao Zedong, and therefore the underlying political philosphy for all of the People's Republic of China today, although it is more apparent in Taiwan today.
The Three Principals stresses the importance of three things
1) Minzu, which refers to nationalism. In order for China to become great, all of the different ethic groups in China needed to be united to push away imperialist nations. Sun believed that China needed to develope a "civic nationalism" rather than an ethnic nationalism to unite people of different cultures (Muslims, Mongols, Tibetians, etc)
2) Minquan or democracy. Sun believed that the power of the government must come from the people. Now although China is communist, the communist party stresses that in Chinese society it is the people whom give China its power. Sun meant democratically elected leaders, but eventually the communist party takes over and changes the meaning of this principal.
3) Minsheng or welfare. This refers to Sun's belief that the ideal Chinese government can provide its people with food, clothing, housing and transportation. These are areas of focus echoed by the government of China today.
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Sun Yat-Sen, seen as the father of modern China, played an extremely significant role in the manifestation of the political revolution of 1911. Increasingly angered by the humiliation that China had to face from the West, he organised traditional secret Chinese societies that sought to overthrow the Qing government and to take authority away from local officials. He was suppressed and sent into exile, where exposed widely to Western political thought, grew to become a famous Chinese nationalist figure in the West. Sun developed his own idea of nationalism, which saw the Chinese having to go through two stages to attain independence- they had to overthrow the Qing dynasty before they could establish a strong, centralised state. He sought to restore the Chinese nation by driving away the barbaric Manchus that formed the corrupt Qing government and he saw revolution as the only means to do so. In 1905, he organised the Revolutionary Alliance, which sought to achieve his aim of an independent China.
The 1911 Revolution started from the Wuchang Uprising, which soon gained momentum and triggered nationalist uprisings all across China. After receiving news of the revolution, Sun returned to China and was elected as the provisional President of the new Chinese republic. In effect, Sun was the only figure in Chinese society who could galvanise the majority of the Chinese population to support the revolutionary cause. He quickly redefined Chinese nationalism and its role in the 1911 Revolution. Sun recognised that distinctions between the Han Chinese and other ethnic groups would essentially mean a potential loss of territories, such as Tibet, Mongolia, and Manchuria, for China, who had only pledged allegiance to the Qing dynasty. He advocated for the creation of a Chinese nation, in which all major ethnicities were included, unifying China. This form of nationalism now played an unifying role and paved the foundations for other nationalistic ideas in Chinese society. Sun also transformed the Revolutionary Alliance into a democratic political party, known as the National People’s Party (GMD), which would form the main presiding party in China for the next few decades.