The term futurist architecture is usually applied to a form of architecture that first appeared in Italy in the early 20th century. The manifesto of Futurism, in which its main principles were explained, was written in 1909.
This style is mainly notable for its interest in, even love of, machines and industry, and there is often a strongly militaristic theme and a love of war (of course this is before World War I made such ideas seem less attractive to many people).
An excellent example is Angiolo Mazzoni's heating plant and main controls cabin at the Santa Maria Novella Railway Station in Florence, designed in 1929 and built in the 1930s.
Later, the Art Deco style, which developed from the 1920s onwards, was also often called futuristic, though it wasn't called Art Deco until much later. A good example of this style is the Chrysler Building in New York City.