The straps attach to the side of the driver's helmet and keeps the head from snapping from the spinal-cord.
For the everyday driver, you're only protection is the air-bad in the steering wheel.
Don’t forget that Earnhardt was killed by a safety belt failure. No failure, no death. Although I think the HANS (or Hutchens) devices should have been mandatory prior to this. It’s just a great idea. Especially in the open-wheel world (F1, IRL, CHAMP) where the helmets had gotten so heavy.