The video above demonstrates what quantisation distortion sounds like, and how dither solves the problem.
And along the way, why you should always use dither when saving 16 or 24-bit files. (In my opinion)
Dither works by randomising the quantisation errors that occur whenever we process audio. (Strictly, it de-correlates them from the input signal).
To do it's job, the dither needs to be random - "fresh", if you like. Digital recording "freezes" the noise so that it's no longer random, and this includes any previously applied dither - which is why it's important to use dither whenever you bounce, export or consolidate at a fixed bit-depth.
Interestingly, it also explains why dither is not always necessary when you first record an analogue signal - most audio has enough random noise in it (hiss !) to effectively "self-dither" the signal. But once it's been recorded digitally, the noise gets "frozen" and the effect stops working, and a new dose of dither is needed every time you bounce, export, consolidate etc - unless you're doing it as floating-point file.
