As defined by Wikipedia, shortwave radio is radio transmission using radio frequencies in the shortwave bands (SW). There is no official definition of the band range, but it always includes all of the high frequency band (HF), which extends from 3 to 30 MHz (100 (exactly 99.930819333) to 10 (exactly 9.9930819333) meters); above the medium frequency band (MF), to the bottom of the VHF band.
Basically, it uses something called radio waves to bounce off ever-changing particles in the ionosphere, which is an ionized(so many big words and links to wikipedia, lol) part of earth's atmosphere(which I'm sure you all know what is, but here you go) ranging from around 48Km(30Mi) to 965Km(600Mi) above sea level and come back to planet earth, "over the horizon" as wikipedia says. This is called Skywave/skip propagation, and it offers a far better range than standard AM/FM frequencies/radios do. Think of it like "pre-internet internet."