It would be a bit obvious to say “a circuit that changes the shape of the waveform going through it”, but that is the point. Waveshapers often have specific goals in mind, such as converting an incoming triangle wave into an outgoing sine wave, or to add tube-like soft clipping to the peaks and transients of waves. Many waveshapers are simply intended to mangle (er, add higher harmonics to) waveforms in interesting ways, creating noisier (er, more complex and bright) harmonic spectra to create new sounds.
