Steampunk is widely called "Victorian science-fiction." Basially, it is a sub-genre of sci-fi that has morphed over the years and now takes many forms. The basic idea is a Victorian-esque (Steampunk has also been modernised and Steampunk stories have taken place either in the present day or in the future, but the aesthtic and feel of the Steampunk world is always Victorian/Edwardian) world, before the likes of Einstein gave us science on an atomic level. The world is powered by steam and gears, cogs and clocks. Devices are clunky and, by today's standards, pretty rudimentary. Think of the scientific advances in the industrial revolution in Queen Vic's days, and now imagine science didn't really much evolve from there.
Aviation is a big deal in Steampunk: air ballons and Zeppelins are an absolute must in practically any Steampunk story. Time travel is also an important theme, especially in the works of H. G. Wells. Robots and other inventions are pretty big too.
Steampunk extends into fashion as well; elaborate headgears with attached monocles, goggles, clunky prosthetics all made up of gears and cogs, and twisted Victorian fashion are all part of the general look.
The most common misconception is that one can simply "stick cogs on something" and make it Steampunk. Take a compuuter and stick some cogs on it voila... not Steampunk. Make an actual, clockwork powered computer with a giant pendulum swinging on the bottom and steam coming from a little pipe at the top, and voila... Steampunk.
So yeah, the basic definition is "Victorian science fiction."