What is a synthesizer anyway?
Synthesizers are instruments that create sound via Waveforms that are further shaped and manipulated by various other external controls to produce changes in tone, timbre, pitch, and time duration.
That above sentence might sound like a bunch of random words strung together, but lets look at synthesizers, or synths, from the perspective of other ordinary instruments that are more familar.
A piano needs its strings and hammers to produce its sound. A synthesizer similarly has a piece that performs that function: its electronic oscillators that produce audiable sound.
One difference between a synthesizer and a real instrument is the relative complexity of the sounds. Traditional Synthesizer sounds are limited by their sound sources, ie oscillators, in that they can only create simple waveshapes, or waveforms. Anything that produces sound in the real world have much more going on acoustically.
To discuss control of pitch, On a piano, playing a key moves a hammer that strikes a string of a particular length which produces the note of your chosing. In the synthesizer context, your keypress introduces a control voltage to a circut that not only make the oscillator sound at the note you play, but also triggers the "gate" that allows sound to emit from the signal path ( or speaker )
Of course, most musical instrument doesn't produce a continuous drone. A violin's sound can fade in, or increase in volume until it its volume is constant. A synthesizer makes use of a transient generator (or more commonly referred to as an envelope generator) to allow the note to have the volume dynamics of real world instruments.