Hub centric rings are the small plastic, or sometimes metal rings that help center the wheel on to the hub. They are not necesary for all aftermarket wheels, and often times are just installed as a last effort to eliminate vibration problems.
Hub rings serve no purpose after installation, their entire job is to hold the wheel perfectly centered while the lug nuts are being installed.
The hub rings sole responsibility is to take up the space between the center bore of the wheel and the hub of the car.
All wheels are classified as being either "Hub Centric", or "Lug Centric." The term Centric refers to the way a wheel is centered. In other words a hub centric wheel centers on the hub of the car, if you put the wheel on the car without lug nuts the wheel would be perfectly centered. On a lug centric wheel, the wheels are centered by the lugs as they are tightened down. Manufacturers build wheels lug centric to allow the wheel to fit a wider selection of vehicles.