The process by which one signal is used to modify another. The controlled signal is referred to as the 'carrier', and the controlling signal as the 'modulator'. It is of the greatest importance in both sound synthesis and signal processing.
The two main parameters of a sound to which modulation is commonly applied are those of amplitude (loudness) and frequency. Amplitude modulation of a signal causes changes in loudness in that signal. If the control signal is a slow regular waveform (e.g. a sine wave) the result is a tremolo - similar to (and often confused with) vibrato, except that there is no pitch deviation. Once the frequency of the modulator is raised above 10 to 15 Hz the tremolo amalgamates into a complex sound with added frequency components derived from the pitches of carrier and modulator. An irregular or transient control signal is generally associated with envelope generation.
Frequency modulation causes the pitch of the carrier to rise and fall according to the shape of the modulating waveform. If this is, as above, a slow regular waveform, the result is vibrato if the depth of the modulation is low, otherwise becoming a wide siren-like effect. If the modulating waveform is a series of discrete steps, the result is a series of discrete pitches. Particularly complex sounds arise when the frequency of the modulator is close to or even higher than that of the carrier. (Source - Richard Dobson (1992). A Dictionary of Electronic and Computer Music Technology. Oxford University Press.)
Ring modulation allows for the sum and difference of two input frequencies to be combined to create a new sound. Often one of these frequencies is at a sub-audio level allowing the creation of a sound of two similar frequencies, frequently with noisy textural characteristics.