A 'no-claims bonus' and 'no-claims discount' are two slightly different terms for the same thing. In essence, for every year that you go without making a claim, your insurer will usually give you a discount at renewal. That's because insurers like less-risky policyholders.
And the more years you go without making a claim, the larger the discount will be. For instance, an insurer may give you a 30-40% discount if you can go without claiming for the first year of your policy, and then give you an extra 10% discount if you're then claim-free in the second year.
You can often also pay to protect any no-claims discount you've built up – read more on how no-claims discounts work.