In a crash it's the speed of the stop that causes most injuries and the HANS device stops the head from snapping forwards or sideways in a severe stop. In the good old days, the large lateral force in a crash would cause the driver's head to be slammed from side to side or forwards and backwards. This was made worse by the added weight of the helmet, making the head behave like a pendulum. Spinal injuries resulted as the neck was over-extended - a severe version of whiplash.
The HANS device is a yoke that sits over the driver's shoulders, and around the back of the neck with a pair of straps up the back that attach to the helmet. When the driver is sitting in the car, where the seatbelt straps pass over the top of the driver's shoulders, they sandwich the HANS device between the straps and the shoulders. As the straps are tightened down, the device becomes held down. In normal use, the straps are long enough to allow the driver to look down and from side to side, but they're short enough that in the even of a crash, as the head moves forward it's held from going too far by the straps.
The entire function of the HANS device relies on the seatbelts - as soon as the seatbelts are undone, the yoke basically just sits over the driver's shoulders which is why it's so easy to put on and take off - you'll see them do it in the pits sometimes.
There are also HANS devices for motorcycle riders and racers but they're a little different. Obviously there's no seatbelt on a motorbike so instead of relying on a belt to clamp the device to the rider's shoulders, this type rely on straps under the rider's armpits to hold the yoke down. From that point on it works exactly the same as the car version, preventing hyperextension of the neck in a crash.
So look for it next time you watch your favourite motorsports and see a driver being strapped into his ride. Most motorsports use them now.
As an ironic footnote, it's worth noting that legendary NASCAR racer Dale Earnhardt refused to wear one, arguing that they were uncomfortable and ineffective. He was subsequently killed in a crash that would have been survivable had he been wearing one, and his death forced the HANS device to become mandatory in NASCAR.
