The Guomindang was Chinese foremost nationalist party, it's name literally meaning The Nationalist Party, which formed the government from 1928-1949 and from then on Taiwan from 1949 until the 1980s. It remains one of the largest parties on Taiwan and is currently the governing party.
The Guomindang was founded by Sun Yatsen in 1911 as a unification of the disparate nationalist and republican rebellions against the Qing Dynasty. Despite achieving its goal of toppling the Qing Dynasty, the Guomindang wasn't very successful early on and was already suppressed following a failed rebellion against the new government in 1913.
A new nationalist awakening and Soviet support gave the party a resurgence starting in the early 1920s. This allowed the party to build its own state with a capital in Guangzhou (Canton), including an army under the leadership of Chiang Kaishek. The purpose of this army was to end the fragmentation that had followed the fall of the Qing Dynasty and establish a national, democratic government. The party suffered from internal divisions, however, due to trying to represent all of Chinese nationalism, from a Communist left wing to an authoritarian right wing based in the military. Before his death in 1925, Sun Yatsen's personal dominance of Guomindang policy kept this in check, keeping official policy close to that of the Communists.
The Guomindang put its army to use for the unification of China with the Northern Expedition in 1926. By 1928, the Northern Expedition had put all but the westernmost regions under the control of the Guomindang. However, it was no longer the same Guomindang. In 1927 Chiang Kaishek carried out a military coup against the Guomindang's civilian leadership and had purged it of both Communists and the left in general. This also meant that ideals of democracy had taken a backseat to the military and conservative cultural values.
During the 1930s, the Guomindang under the leadership of Chiang Kaishek maintained control over the majority of China and became the formal leader of the Chinese resistance to the Japanese invasion after 1937. Following the end of the second world war, the Guomindang lost the civil war to the Communists and was driven in exile on Taiwan.