This wasn't a topic I was planning to cover but the question came up on a message board I am on so I thought I would share my thoughts here as well. First what is posterization?
Posterization of an image entails conversion of a continuous gradation of tone to several regions of fewer tones, with abrupt changes from one tone to another. This was originally done with photographic processes to create posters. It can now be done photographically or with digital image processing, and may be deliberate or may be an unintended artifact of color quantization.
The tricky part is, this isn't something your histogram can show you, you aren't blowing any channels to make this happen. You have to learn to look for it and then change your editing as needed to undo/prevent it.
Here is an image I took on Saturday of a bright pink flower, which is a common color to have this issue with. You can see my my LR edits (this was a little underexposed SOOC but I was just messing around when we were in Georgetown), this is my final edited version
click for larger
Here is a screen capture of the detail in the petal of that flower
You can see the gradual change in color here.
Here is an edit where I just did my import preset (and no white balance edit) and tried to pull the exposure up. I have the red for blown highlights turned on and you can see nothing is blown (some darks are clipped).
You can see something funky is going on with that petal we had just zoomed in on above.
Lets zoom in again.
Now you can see the posterization.
I don't really know enough about how to not make it happen in editing, other than to recognize it, watch for it and undo whatever you just did that created it.