Synth-pop, as a Discogs style tag, can apply to pretty much any pop music dominated by synthetic sounds. Before non-electronic music was allowed in the database, the tag was applied quite liberally in order to justify the inclusion of dance records from the pop and R&B club scenes, and is still used fairly broadly.
The synth-pop genre, though, primarily originates in late 1970s/early 1980s New Wave, the post-punk "alternative" rock movement that encompasses a wide range of styles and attitudes. There are some non-New Wave synth-pop bands like Pet Shop Boys, but on the whole, the synth-pop scene of the 1980s was dominated by a faction of New Wave bands that embraced the use of electronic instruments and relatively light, dance-oriented songwriting, yet still retained a fairly typical four-piece rock-band structure (percussion, lead instrument, bass instrument, vocal). Most synth-pop combines electronic and other instruments, plus strong vocals and melodies, and elements of whatever dance music styles are popular at the time. The music generally isn't very experimental, serious, or dark, but some synth-pop bands like The Human League and members of the "minimal wave" scene explored a more alternative, moody sound at times. Synth-pop enjoys revivals now and then, with new bands deliberately paying homage to the old sounds, or just stumbling onto a similar aesthetic in their experimentation with styles.