This movement is internationally significant in that a formal declaration of independence is one of the three conditions under which the PRC has stated that it will take military action against Taiwan (the other two being that Taiwan develops an atomic bomb, or if Taiwan comes under 'foreign interference'). This would raise the possibility of an intervention by the United States under the Taiwan Relations Act and the possibility of a superpower conflict in East Asia.
This movement began under the Japanese, and was ironically supported by Mao Zedong in the 1930s.
After the Kuomintang began to rule the island, the focus of the movement was as a vehicle for discontent from the native Taiwanese against the rule of "mainlanders" (i.e. people who came over with Chiang Kai-shek's armies and government in the late 1940s). Between 1949 and 1991, the official position of the government on Taiwan was that it was the legitimate government of all of China and used this position as justification for authoritarian measures such as the refusal to hold parliamentary elections. The Taiwan independence movement intensified in response to this and presented an alternative vision of a sovereign and independent Republic of Taiwan. This vision was represented through a number of symbols such as the use of Taiwanese in opposition to the school taught Mandarin Chinese. Taiwan independence has been some of the motivation behind the Taiwanese localization movement.
In more recent years, the focus of the movement has changed to that of insuring the sovereignty and dignity of Taiwan against the possibility of rule by the People's Republic of China, and as such has been more willing to take on the symbols of the Republic of China. The movement has also moderated in recent years because of decreasing friction between "Mainlander" and "native" communities on Taiwan, increasing economic ties with the Mainland, continuing threats by the People's Republic of China to invade if it declares independence, and doubts as to whether or not the United States would support a unilateral declaration of independence. Since the late 1990s, supporters of Taiwan independence have argued that since Taiwan, as the ROC, is already independent from the mainland, a formal declaration of that fact is unnecessary.
Opinion polls suggest that between 70 to 80 percent of Taiwanese support the "status quo" which is to leave Taiwan's status exactly the way that it is. One advantage of this option is that it avoids the necessity of defining exactly what Taiwan's status really is.
See also: Politics of Taiwan