Every acoustic instrument, however different they otherwise sound, shares one thing in common: they all produce sound through a physical vibration — a plucked or bowed string, a column of air set moving inside a wind instrument, or a struck drum skin, with that vibration then propagating through the surrounding air as the sound wave a listener actually hears. Electronic music production breaks from this entirely: a synthesizer generates a waveform directly as an electrical signal, with no physical string, air column or surface vibrating to produce the underlying sound at all, until that electrical signal eventually reaches a speaker and is converted into actual physical vibration at the very last step.
The waveform is built mathematically, not extracted from a vibrating object
Where an acoustic instrument's sound is shaped by the physical properties of whatever object is vibrating — a string's length, tension and material; a wind instrument's bore shape — a synthesizer instead builds its waveform electronically, typically starting from simple, mathematically well-defined basic waveforms, such as a smooth sine wave or a sharper, buzzier sawtooth wave, and then shaping that raw waveform further using electronic circuits or software processes that control how its volume, tone and pitch evolve over time. Because the starting waveform is generated electronically rather than being a byproduct of some specific object's physical vibration, a synthesizer can, in principle, produce timbres that no acoustic instrument, bound by its own physical construction, could ever actually produce.
The same underlying electrical signal can still be manipulated in real time
Despite generating its base sound electronically rather than acoustically, a synthesizer still gives a performer or producer many of the same kinds of real-time expressive control an acoustic instrument offers, just implemented differently — a synthesizer's electrical signal can be shaped in real time using filters, which selectively emphasise or reduce specific frequency ranges, and envelopes, which control precisely how a sound's volume rises and falls over the course of a single note, giving an electronically generated waveform much of the same expressive shaping and character an acoustic instrument's physical construction would otherwise provide, just achieved through electronic means rather than physical ones.
What we're still unsure about
The basic distinction between acoustic instruments' physically vibration-based sound production and a synthesizer's directly generated electrical waveform is well-established, uncontroversial audio engineering. What's more a matter of ongoing aesthetic and musicological debate than settled fact is how meaningfully electronically produced sound differs, in genuinely perceptual and musical terms, from acoustic sound once it's been reproduced through the exact same speaker at the listening end — some listeners and researchers argue electronically generated timbres retain a perceptibly distinct character even after that final conversion step, while others argue the distinction becomes considerably less meaningful once both kinds of sound are travelling through the air as the same kind of physical vibration, a genuinely open question in music perception research rather than one with a single settled answer.
This sits inside Electronic Music Production, one of seven topics in Composition, one of four domains in Music, one of seventeen subjects the app can quiz you on.