Right, but want makes you say Clarity is post processing?
If one were to apply non-linear contrast adjustments prior to demosaicing, that would create huge problems. That's why it much more practical to do these adjustments on post-demosaicing data. Once the data is in RGB space we can post-process it any way we want. Unless someone like Eric Chan tells us it is not, we can consider Clarity as post-processing that takes place on the demosaiced RGB data.
One common characteristic of images that span a large range of contrast, is that they may look rather flat, lifeless. Instead of a simple S-curve like adjustment (Clarity) mostly to the mid-tones, which can lead to ugly halos if pushed too far, the Topaz Clarity plugin is much more clever, and it allows to (adaptive to local contrast) adjust gradients that span different ranges of contrast and different size.
It is difficult to describe the effect, because it adapts to local contrast which is different in every image, so it's best to try for oneself, on one's own images. The real-time update of the preview helps to judge the creative effect quite well. As always, it's easy to go completely overboard with such tools, but with the proper amount of restraint it can do wonders in the hands of a master.Here is a demo video
that does a reasonable job of showing the different features.