The mechanics of a wolf tone are basically this:
Everything has a natural resonance frequency… the pitch at which it vibrates. This is what causes a wine glass to shatter if someone sings the right high pitch.
A wolf tone happens when the note you’re playing is close to, but not exactly, matching the natural resonance frequency of your instrument (on cellos, this usually shows up around E to F# on the D string).
The way we compensate usually involves offsetting that wolf tone with a small weight either on the string below the bridge to offset that pitch, or glued on the instrument itself.