The Weimar Republic had two major political offices: the President and the Chancellor (i.e. Prime Minister). In January 1933, Adolf Hitler was appointed chancellor, while the office of president was held by Paul von Hindenburg who at the time was too old and senile to be a real political force.
In March 1933, the "Enabling Act" was passed, allowing the chancellor to wield legislative and executive power without support from either the parliament (which soon ceased convening) or the president. Hindenburg still had the theoretical power to appoint a new chancellor, however. When he died in August 1934, therefore, no new president was elected. Instead the two offices were merged into one, and the name Führer was invented for it.
By the way, "führer" also means "driver" and "tourist guide". Since 1945, the usage of the word has declined somewhat.