I just threw this graphic together to explain how the most common synthesizer topology works. I am working on a few posts that will actually explain what these things means but I'll just vaguely describe it here for a bit.
An oscillator is just a circuit that repeats a pattern of voltages over and over. In a very general sense, how fast it does this is what we interpret as "pitch". A VCO, or "Voltage Controlled Oscillator" is an oscillator that can change the pitch it produces when controlled by some other circuit providing a control voltage.
Usually for this topology one will pick a VCO that produces what we call "harmonically rich" waveforms. What that means is that there is energy on lots of frequencies high and low. The pattern of this distribution of energy over frequency is what makes a trumpet sound like a trumpet and not a piano. This is the sensation that we call "timbre". The "subtractive" in "subtractive synthesis" refers to taking a signal with lots of energy all over the place and then removing, or filtering out, some of it so that you can change it to whatever sound you want. The opposite is "additive synthesis" where you take a whole bunch of signals that barely have any harmonic content and then just add them all together.
Anyway, there are usually only a handful of timbres that a VCO can produce. A VCO is usually followed by a filter so that you can achieve a much greater variety of timbres. You can think of a filter like the equalizer on a stereo system, in general, but for synthesizers the most ubiquitous filter is a "low-pass filter with resonance". Your stereo's equalizer has several frequency bands that you can boost or cut to change the sound. A low-pass filter is like this except you get to name a precise frequency. Then everything below that frequency is kept and everything above that frequency is lost. It actually has a rounded response curve to it, which can be made more steep by increasing the number of "filter poles".
"Resonance" means that in addition to cutting the energy above the named frequency, the filter boosts content RIGHT AT that frequency. These are the two most common controls for a filter: cutoff frequency and resonance. By making a filter whose cutoff frequency and resonance are controllable by separate circuits that merely provide a "control voltage", you can make something called a VCF. A "Voltage Controlled Filter".
After that description I'm sure you can imagine that a VCO+VCF can produce a very wide variety of sounds! But there is one problem. When you turn on this basic synthesizer, it will start making noise, and it will continue to make noise until you turn off the power. Furthermore, all of the sound it makes will consistently be of the same volume. This is why you need a Voltage Controlled Amplifier!
A VCA is even simpler than a VCO or VCF. It takes a control voltage input and that level becomes the volume. If you want silence, you put in zero volts, and if you want it loud, then you put in lots of volts. There are special circuits that output control voltages designed to make a VCA mimic the volume-variation characteristics of particular instruments--these and other control voltage sources are what really turn this synth topology into a "real instrument"!
I will go into further detail about VCOs, VCFs, VCAs, subtractive and additive synthesis techniques, definitions of pitch, timbre, volume, etc, and types of control voltage-generating circuits in later posts--I just wanted to throw that diagram out there to make sure I knew how to make one.