Simply, a temperature controller keeps a WSM at a constant temperature by controlling how much air gets to your lit fuel.
They all do the same thing, but a little diferently.
Like the Auber, my iQue 110 has a temperature probe that goes in the cooking chamber. That tells the controller what the temp is where the meat is. The controler then uses a variable speed fan to speed up or slow down the flow of air as needed to maintain your desired cooking temperature.
On a WSM, you close down two of the three bottom vents completely, and the temperature controller attaches to the third vent, which is wide open.