Steampunk is an artistic and literary style that tends to take place in fictional alternate realities, typically Victorian era, or American Midwest, where high technologies are made possibility through the use of steam engines. For example, steam powered computers, steam powered tanks, steam powered mechas and steam powered arm-machine-guns are all possibilities, provided you don't ask too many questions or look TOO deeply into the physical possibilities. This results often times in a world that appears outwardly advanced, but is rife with corruption.
Steampunk was popularized in novels by preeminent writers, such as Jules Verne in his flagship masterpiece "30,000 League Under the Sea." It has inspired a number of spinoff genres, such as "dieselpunk" and "Cyberpunk" both of which take distopic influences from Verne's work.