Ring modulation is a way of combining audio signals. Ring modulation works by multiplying two signals, where one is typically a sine-wave. Interesting harmonics can be generated by carefully selecting and changing the frequency of the two input waveforms.
On the C64 SID chip, ring modulation multiplies a triangle wave with a square wave.
A ring modulator was a common feature on early modular Moog synthesizers. The ring modulator went out of fashion with the advent of all-in-one synthesizers, but has returned as a feature in digital modelling and software synthesizers.