Steampunk is perhaps an over-used term in places, but it seems to suggest anachronistic or alternate-path technologies, where things that weren't invented or widely used in our historical past are given the ability to exist through the use of old-looking technology.
Steam isn't integral to Steampunk as a genre, despite steam being in the title. In the high-profile Steampunk novel The Difference Engine, included among the contraptions that made Victorian England more technologically complex than it historically was, was the titular Engine, a derivative of Charles Babbage's own calculation device. While it may or may not use steam to power its immense cogs, it is fundamentally a mechanical system, and as such, the alias clockwork has been connected to this article to include things which, while still using anachronistic styles of technology, don't necessarily use steam to power them.
This use of a realistic way to power such machines, though, should not dissuade one from thinking that it is still often just another form of magic and the creation of a mood. Often the steam engines depicted in games and other fiction don't have robust designs-- you will often find a steam-driven machine would get way too hot for people to stand next to, due to the overwhelming heat needed to keep a boiler running and producing steam (that in turn creates motion).
What's ironic about the very term Steampunk, however, and something pop culture fans should keep in mind, is that in essence, we still live in a steam-driven society. Nuclear power itself is, in a sense, a steam-power technology. Its power source comes from the decay of atoms and the reactions this causes, but ultimately, it's just a way to generate heat, which excites the molecules in a boiler, to make steam that runs turbines, similar to the stuff that Steampunk uses. While coal is often said to be the appropriate power source for steam technology, it needn't be.
This brings us to what is perhaps the fundamental assumption that Steampunk inventions really make: it is not so much about the power source, or about steam itself, but instead that the electronic age, with its microcomputers and digital circuitry, is bypassed. In Gibson and Sterling's Difference Engine, the calculator is centralized and IMMENSE, because it has to be. Mechanical parts can only be so small before they break too easily. Unlike with electronics, which follow Moore's Law, mechanical devices are more limited in their ability to improve in portability. This creates design aesthetics that are often immense and strange, lending to an alien-yet-familiar-feeling that is integral to the use of steampunk devices.
In sum, what magic does for some types of fantasy, and advanced electronics do for science fiction, steampunk accomplishes through a different route, creating an appealing alternative that allows for machines without the fundamental fantasy to be sullied by technology that's too commonplace to be interesting.