Synth Pop
Exactly What It Says on the Tin.
Synth Pop is what occurs when you take synthesizers and make pop music with them.
An important stylistic mark of Synth Pop is that the synthesizers deliberately sound like synthesizers, or in Purple Prose they exploit artificiality. Synth Pop does not use synthesizers to replicate acoustic sounds but rather as instruments in their own right.
Synth Pop can use acoustic instruments, however the majority of the work must be Electronic Music in order for a pop song to be classified as Synth Pop.
This genre was very influential during The Eighties. Whilst many eighties pop bands were not predominantly electronic, they were usually significantly electronic and made generous use of of their synthesizers and drum machines.
The distinction between this genre (at least during The Eighties) and New Wave is not easy to establish. One potential distinction is that Synth Pop must be predominantly electronic, and significantly electronic pop music can be classified as New Wave. However, some people do tend to use "New Wave" and "Synth Pop" more or less interchangeably, and use either term to refer to any eighties pop song with a significant electronic component.
Significant artists include Kraftwerk (the Trope Maker), Yellow Magic Orchestra (Trope Codifier and depending on who you ask Trope Maker,) New Order, Gary Numan, Depeche Mode and arguably a good portion of The Eighties pop acts in general (who are either this or New Wave).
There's also been a resurgence of synth pop in the indie arena, taking its cues from early 80's new wave (You know, keyboards and depression, together in perfect harmony. Leads to artists with names like Casiotone For The Painfully Alone.)
The Darker and Edgier, more aggressive and punk-like approach to this style of music results in Electronic Body Music or EBM, which is a subgenre of Industrial.
The darker, angstier, Wangst-ier (depending on your mileage) and Goth-oriented version of this style of music is called Darkwave.