Actually, Kaiser Wilhelm II did not "fire" Otto von Bismarck. Rather, Bismarck surrendered his office as a result of his conflicts with the Kaiser. The Kaiser obviously drove Bismarck out of office yet did not really fire him. Bismarck left office in March of 1890.
Otto von Bismarck had come to control in Prussia in 1862. By then, Germany was not yet joined together and Prussia was an autonomous nation. Bismarck needed Germany to bring together and battled a progression of wars to make this happen. At the point when Germany bound together in 1871, Bismarck moved toward becoming chancellor of the new nation.