The classic, electro-mechanical way of generating a reverb effect in a small box. (There's also plate reverb and dedicated reverb rooms, but a reverb plate is a huge contraption and a reverb room takes up, well, an entire room. Reverb plates and rooms have largely been replaced by ultra-expensive Lexicon electronic studio reverb processors.)

Spring reverb works by turning an electrical signal into a mechanical wave, i.e. a vibration, that travels down a spring suspended in a soundtight housing. Usually, it is a torsional wave, not a longitudinal or transversal one; it is created by basically twisting one side of the spring back and forth, either by something like a speaker driver connected to a lever or by what is essentially a little permanent-magnet electric motor. In tech speak this is a rotary transducer. At the other side of the spring, another transducer picks the wave off the spring and turns it into electricity again.

What one has now is a delay line, i.e. something that swallows up a signal and spits it out a split second later, which is, for the signal, pretty much an eternity. Due to various physical characteristics of a spring's torsional vibration, the sound is not just delayed, though; vibrations are mixed, reflected, damped etc. -- the result sounds reverb-ish, although it's a far cry from real natural reverb.

Many guitar amps still have spring reverb, and so have organs (such as certain Hammond models) and some rotary speaker cabinets. Shaking a spring reverb unit can cause very, very ugly sounds, but has been done as a special effect. (Just so you know what exactly Keith Emerson was up to when he rocked his Hammond back and forth.)