Hi April, "clarity" changes the appearance of the image by altering the mid-tone contrast and making it appear sharper. This is different to the "contrast" slider which alters the contrast of the whole image to achieve the same thing. Clarity is, therefore, a selective sharpening tool, although you can't choose which parts are going to be affected.
This can be a bit hard to see sometimes, depending on the subject matter and the number of pixels containing mid-tone colours. As far as I can tell, from using both CS6 and Lightroom 4, there's little difference in the visual effect of this slider.
Hope that helps