Modulation means change.
In music, modulation is often used to mean a change of key. Modulation in synthesis means something different, a change in timbre.
Modulation synthesis is the process of changing the timbre of a sound. The mechanism by which modulation synthesis works is to use one sound to modulate (change) another sound. Modulation synthesis requires a minimum of two sounds as inputs. The input sound doing the changing is called the modulator, the input sound being changed is called the carrier. The terms, modulator and carrier, are throwbacks to the days when modulation was used in AM and FM radio.
Modulation synthesis uses a modulator to change either the amplitude or the frequency of a carrier. There are two types of amplitude modulation, Ring Modulation (RM) and Amplitude Modulation (AM), and one type of Frequency Modulation (FM).
Modulation synthesis is simple or complex. Simple and complex are technical terms. Simple modulation occurs when both the modulator and the carrier are sine waves. Everything else is called complex modulation. The terms, simple and complex, refer solely to the inputs of modulation, not the output. Simple and complex modulation both generate a sound output with a rich timbre.