A totalitarian movement started and popularized by Benito Mussolini which, much like communism, stresses the state as the cure for societies problems.
What differentiates it from Communism is the focus on nationalism more than the workers.
Nazi Germany was inspired by fascist Italy, though there are some differences. Its Nationalism extends into racial superiority as a distinct tenant.
There is a misconception of Communism and Fascism being on different ends of the political spectrum, this is a myth created by the Soviets to brand enemies of the party (the fascists were competition).
Fascist and Communist states both supress the individual for the collective people, and in turn socialize health care, business (sometimes corporatism), and education.
Fascism is not inherently left or right wing but it shares its roots with modern liberal ideology, as well as in eastern spirituality (that's where Hitler got the swastika from) and marxism; not to mention a general disdain for all things Judeo-Christian (Il Duce, Hitler, Lenin, Stalin, Pol Pot and Mao all had an equal hate for Christianity).
That isn't to say that there isn't right wing fascism...its just harder to find. The most famous fascists, Hitler and Mussolini, were definitely on the left side of the spectrum.
These smoking bans are fascist.