In practical terms, that means a single small device — often no bigger than a USB stick — can let you listen across a huge range of frequencies, switch between modes (AM, FM, SSB, CW, digital) at the click of a mouse, and even watch the radio spectrum as a live, scrolling "waterfall" display. The same hardware that tunes a shortwave broadcaster this minute can decode an aircraft's position the next.
Because the cleverness lives in software, SDR has thrown the hobby wide open. A newcomer can be listening within minutes of plugging in an inexpensive receiver, while experienced operators can build elaborate multi-receiver, networked listening posts. The spectrum becomes something you can see and explore, not just hear.
The hardware side
SDR hardware ranges from low-cost USB dongles to high-performance direct-sampling receivers with 14- or 16-bit converters. Many can be used right at your desk over USB; others are designed to sit by the antenna and stream over your home network.
The software side
The software is where you tune, filter, demodulate and decode. Modern SDR applications give you a spectrum view, a waterfall, recording, and plug-in decoders for digital modes — turning raw radio into something you can read, map and enjoy.