Synth is short for synthesiser, those boxes of electrical circuitry that have been adding swishes, bleeps, and pulses to popular music since the instruments became more affordable and thus more accessible in the late 1960s. Synth Pop as a genre really exploded in the early 80s with the arrival of small, versatile keyboards and a range of programable drum machines.
While Kraftwerk (Germany) and Yellow Magic Orchestra (Japan) are considered two of the major influencers, it was a UK scene that included Gary Numan, Japan, Ultravox and Depeche Mode that really spread the synth word through the clubs of Britain and up charts across the world.
The style really was international. In addition to a flock of UK artists (Eurythmics, OMD… the list goes on) we bopped and popped to hits from Switzerland (Yello), Australia (Icehouse), Belgium (Telex), and even the USA (Devo).
Though the 80s were its day-glo heyday, synth-driven pop has far from disappeared, with bands continuing to explore diverse hybrids of electronic sounds and pop music. And it will doubtless continue as long as we have power points and synthesisers to plug into them.