This output signal is the sum and the difference from both inputs, and leaves the original frequencies out.
It is an ideal module for producing metallic or bell-like sounds, but you can also (re-)create other weird sound-effects with it, like for example the distinctive "Daleks"-voices from the classic Dr. Who series, created in 1963 by the BBC Radiophonic Workshop.Besides voices, you can also input all kinds of other (amplified) instruments through the ring-modulator.
The Doepfer A-114 Dual Ring Modulator is in fact two ring-modulators in one, which makes it even more flexible. Theoretically you can use the output of the first ring-modulator as input for the second one. The A-114's manual has some nice other examples on how to start patching, but with a bit of imagination you will quickly come up with your own ideas.
You can find some more interesting ring-modulation (DIY) info HERE