As far as I know....
Quantization refers to more than MIDI time-syncing. In general, it refers to grouping things into discrete units.
Say you want to rate your rack gear on a ten-point scale, using only whole numbers. One reverb may rate a 7 in your book, and another may rate a 7.4. Since you're only using whole numbers, this rounds down to 7. This is a type of quantization. It's also a type of distortion, as your rating scale cannot discern the difference between your two reverb units, and calls them both a 7.
In digital audio, quantization is what happens when you run DSP on your tracks. It's most noticeable on fadeouts and reverb tails in 16-bit (hence the old Sound Forge included a dithering option for certain volume envelopes, to counter this quantization noise). It's the sound of your track's bits being quantized-- the sterile, brittle, harsh, cold "digital sound" is the sound of bad and/or too much DSP. (Trust me, I know it all too well!

) This isn't so noticeable in 24-bit due to the greatly increased resolution. Bit depth sort of means that there's only so many discrete volume levels that can be represented -- sort of a larger version of the rack-gear rating scale. A process that wants a sample to say "22.6" will call it "23" instead.
You can see this happen in a wave editor by taking a nice pure 16-bit sine wave and reducing the volume greatly (keep it out of the noise floor though!!) and then increasing the volume back again. The nice sine wave now has little steps in it, and sounds different.
This is my understanding at least.... I'm sure a Bear will eat me if I'm wrong.
Sonusman had a big thread a while back on this that's great stuff.
http://www.homerecording.com/bbs/showthread.php?s=&threadid=48346&highlight=QUAN+errors