Hands up who can really hear dither?!
You! ...as soon you learn what to "look" for. Nobody really perceives "dither", but you can hear it when it's not been applied properly.
What you can perfectly hear is Quantization Distortion. It happens as soon you reduce the precision of a discrete signal (which means "digital" or "stepped"). For example from 24bit to 16bit, or when an analogue signal hits an AD converter.
Such a kind of conversion is simply done by "throwing" away the lowest bits, effectively reducing the amount of decimal places used to describe each sample. As mentioned above, we're talking about really low volume signals, the lowest your bits can carry. And here's the nasty part: Such a truncation introduces a very ugly type of distortion, one that adds very non-musical and easily perceivable periodic garbage. This kind of distortion is nearly impossible to remove and it builds up with each conversion. The latter happens much more often than you may think: For example, most of todays plugins use 64bit floating point precision for their internal calculations - but nearly all DAWs are still running with a 32bit floating point precision. It's not unusual to see 50 plugins on a mix, you'll have at least one truncation step per plugin - the added distortion will be low for each instance, but the distortion pattern will always look exactly the same and will sum up. In theory. Thank god there's a cure for it.
There's a very easy method to reduce the patterns/images created during truncation. All you have to do is to add a very small random signal ("noise") to the file BEFORE truncation. This breaks the periodic nature of these patterns and basically "exchanges" them with noise. This small random signal is called "Dither". It's works nearly perfect if done right (so much that you can hardly hear the difference between the 24bit original and the 16bit CD version).
Ok, I still haven't answered your question.

Dithering shouldn't be audible, so it's a good idea to get familiar with the bad side. Do a simple experiment:
1. Take a 16bit or 24bit file with a huge fade-in or fade-out.
2. Save a copy in 8bit, DO NOT USE any bit-depth converters, just keep it raw.
3. Listen! Compare the original with the low-bit version, closely listen to what happens as the fade attenuation gets stronger..
Now, do the same thing as before, but add an 8bit dithering to the original before you save the file in 8bit.
Compare both 8bit versions. Now don't tell me you can't hear the effect of dither.