Oscillators are the source of digital signals. Once a signal is generated, it is then processed and sent to an amplifier where you can set the volume envelope with ADSR. Often, synthesizers have more than one oscillator allowing multiple signals to be generated in accordance with the parameters that are set on each oscillator.
Additive and subtractive synthesizers generate their sound by allowing 2 signals to be processed simultaneously through amplitude envelopes and filter parameters. The combination of signals along with filter modulation is what produces this particular type of sound from additive and subtractive synthesizers.
Running oscillators in parallel this way can produce some very interesting textures created through layering and filtering. When oscillators are routed in series, they take on different jobs. One oscillator becomes the carrier of the signal and the other oscillator becomes the modulator of the carrier’s signal. Oscillators that can be switched between carrier and modulator are referred to as operators to signify its distinction between a basic oscillator, whose job is to just produce a signal without the ability to become a modulator.
The carrier wave will generate the sound while the modulator wave will modulate the frequency of the carrier wave generating harmonic content. With this routing, the modulator volume dial becomes very sensitive and when used excessively for FM (frequency modulation) can completely change a sound.
When you begin working with synthesizers with more than 2 oscillators, the layering, filtering and frequency modulation possibilities become endless, creating great flexibility in sound creation.
Other types of synthesis generate their sound via different sources yet the modules (oscillator, filter, lfo, amp, etc..), routing capabilities and global parameters are essentially all the same.
To name the common types of digital synthesis, there is additive/subtractive, frequency modulation, wavetable, ring modulation and granular. Each type of digital synthesis will create very different fundamental sounds that are easily routed and manipulated with the parameters included within a synthesizer!