Why An ADC has to round each sample to the nearest quantization step, and when the input is small or slowly varying that rounding error is correlated with the signal, producing harmonic distortion and "stair-step" artifacts rather than benign noise. Adding a tiny amount of random noise (typically on the order of one LSB) before conversion randomizes which step is chosen, so the error becomes uncorrelated broadband noise that the ear or a digital filter handles much better. Averaging many dithered samples can even recover detail smaller than one quantization step, effectively increasing resolution.
Watch out The choice about the converter being unable to settle describes instability or metastability in the comparator, not dither; the one about irregular step size describes differential nonlinearity, an ADC accuracy defect.
Dither = deliberate dirt: add a little noise on purpose so quantization error sounds like hiss, not distortion.