Otto Von Bismarck was forced to resign on March 18th, 1890. His resignation was demanded by the new Emperor of Germany, Wilhelm II.
Von Bismarck and the Emperor clashed over many things which led to his dismissal. Among them were:
Wilhem's youth, relative inexperience, and close relationship with Bismarck as a boy made Bismarck think he could control Wilhelm, leading to Wilhelm's resentment.
Wilhelm's advisors and sycophants in court told him that he would never be a great leader if he had a dominant Chancellor
Bismarck's and Wilhem's views on social policy. Bismarck was strongly in favor of anti-socialists laws, while Wilhelm favored a more moderate approach. Bismarck admitted he wanted a violent confrontation to put down socialist agitation once and for all, which Wilhelm found intolerable.
Wikipedia's article on this is very strong and well researched. View it here.
Technically, Kaiser Wilhelm II did not “fire” Otto von Bismarck. Instead, Bismarck resigned his office because of his disagreements with the Kaiser. The Kaiser clearly pushed Bismarck out of office, but did not actually fire him. Bismarck left office in March of 1890.
Otto von Bismarck had come to power in Prussia in 1862. At that point, Germany was not yet united and Prussia was an independent country. Bismarck wanted Germany to unify and fought a series of wars to cause this to happen. When Germany unified in 1871, Bismarck became chancellor of the new country.
The beginning of the end for Bismarck occurred in 1898. In that year, Wilhelm II took the German throne when his father died after having only ruled for a few months. Wilhelm was very young (only 29) and wanted to make his own mark on Germany. He clashed with Bismarck over foreign and domestic policy. Most importantly, he wanted Germany to have a more aggressive foreign policy, one in which it would achieve its “place in the sun.” Because of these disagreements, Wilhelm II forced Bismarck to resign in March of 1890, less than two years after Wilhelm had taken over as emperor of Germany. Many historians believe that Wilhelm’s more aggressive foreign policy after he removed Bismarck was a major cause of World War I.