A cent is one hundredth of a semitone. Twelve semitones make an octave, so an octave is 1,200 cents.
Why tuners use cents
Hertz values double each octave, so a 2 Hz error is large on a bass and tiny on a violin. Cents measure the error the same way at every pitch.
How much can you hear?
Side by side, trained ears notice around 5 cents. Two strings played together beat audibly at 2–3 cents. That is why TuneBalance's default tolerance is ±3 cents.