A non-claim bonus can also be termed, and is usually called, a no-claims bonus (NCB). It is a discount that seems to be used more prevalently in the UK and other countries outside the US but is catching on with some US insurance companies as well.
In the UK, a no claims bonus is a discount given by an insurance company to a policyholder who does not have claims on their policy. Typically the discount starts around 15% for 1 year of no claims and can reach up to 65% after 6 or more claim-free years, depending on the insurance company's guidelines.
So in general insurance companies reward those who have not made claims against their policy with a discount. The more years a policyholder goes without having a claim, the better the discount will be for the car that the motorist is insuring.
If a driver goes many years without a claim and then places one with their insurer, the no claims bonus might only be bumped back and not completely wiped out depending upon how the insurance provider's NCB system is set up.