Sound synthesis is the process of combining two or more sounds. Noise is a generated random signal. Noise is a collection of signals with random amplitudes and frequencies within specific parameters over time. A filter is a sound modifying module that reduces or eliminates the amplitude of frequency ranges.
Subtractive synthesis is a sound generating process. We pass a sound generating module into one or more filter modules. The filter modules remove parts of the signal. The result is a sound with a unique color. We most often use noise signals to start with in subtractive synthesis. Rich sounds, such as sawtooth waves and rectangle waves, can provide interesting starting points as well.
An example of natural subtractive synthesis is the human voice. When we make the sound "shhh", we change the shape of our mouth, tongue, and throat to soften and remove parts of the otherwise white noise sound.
Like additive synthesis, the filtering properties -- frequency, amplitude, and phase -- can vary over time. The properties may also vary in space. Subtractive synthesis is often cheaper to calculate than additive synthesis.