What is shortwave radio?

Shortwave radio was so-called during the early days of radio because the wavelengths used were shorter than the prevalent longer wavelengths used at the time. Such wavelengths can travel much further than FM, MW and LW by bouncing off the ionosphere.
This permits the listener to pick up radio stations beyond the horizon and from across the globe.

Shortwave radio is used for international broadcasting with many governments using it as a way of putting forward their view on world affairs. Amateurs or Radio Hams can often be heard chatting on wavebands reserved for amateur use. There are utility stations broadcasting weather reports and coded diplomatic messages between embassies. Number stations can also be heard on shortwave. These stations broadcast numbers or NATO call-signs at regular points during the day and are believed to be coded messages broadcast to spies on active service in foreign lands.

Shortwave radio can be heard on frequencies between 1612 and 30000 KHz. A radio with continuous tuning between those frequencies is desirable so that all bands, including amateur and utility bands can be received. Also, you will need Single Side Band (SSB) capabilities for those broadcasting (usually Radio Hams) on this variation of AM broadcasting.