The purpose of a clearing tank is obvious. Homebrewers insist on calling them secondary fermentors, which confuses people. I can think of only two commercial brews that undergo secondary fermentation (I'm not classifying bottle conditioning as a secondary fermentation here). And the only homebrew I make that goes into a secondary is my barleywine, although there are other styles when you add fermentables and do a second ferment.
A clearing tank is used to let the ale settle. It can also be used for dry hopping.