Dither = Good noise to mask bad noise (quantisation errors).
During the render of an audio file, you will need to reduce the bit depth, unless you're rendering at 32-bit (which doesn't require dither).
Bit Depth = The amount of dynamic range between the quietest and loudest level possible.
Reducing the bit depth introduces quantisation errors into a signal, dither introduces noise to mask these errors.
You can reduce the bit depth of a sine wave, and with an analyser open, see the quantisation errors. These errors look like harmonic distortion, a bunch of peaks occurring towards the top end of the frequency spectrum. Dither adds in what you can think of as white noise, which smoothes out those peaks and masks the noise they produce. This is called auditory masking. Auditory masking occurs when the perception of one sound is affected by the presence of another sound.
MV: I've read that dithering removes the noise caused by quantisation errors, rather than merely masking it.
POW Dither Options in Ableton = Psyscho-acoustically optimised word-length reduction.
In the digital domain, 1's and 0's store audio information, and bit depth is the length of that number. Higher numbers equal more bits captured.
If you load a 16-bit file into Ableton and change the volume, Ableton converts it too 32-bit to process. This is true of most D.A.W.'s if they operate at 32-bit floating-point.
32-bit files have headroom over 0dB. If you export a 32-bit file that's clipping, you can reduce the volume of said file, just like using a D.A.W. Fader. The clipping is not permanent to the file like on 16 or 24-bit files. The 32-bit file stores more numbers, or bits, giving you extra headroom.
32-bit files hold twice as much information as 16-bit files.
You should only dither once, as otherwise, you'll increase the volume of the noise added, each time you apply dither.