Please forgive me if the terms aren't 100% correct.
Different insurers do their calculations differently, but this is my understanding of the basic process:
No Claims Discount, normally rated in years, is a discount given which insurers apply to your actual calculated 'rate' or risk.
Different insurers use different amounts for the years earned - no consistency.
Your Rate or Risk is calculated based on some industry calculations tailored by individual insurers, which consider what is the likelihood of having to pay out to you, and is based on many factors including age, location, what you are insuring, and whether you have had any losses/accidents previously among many other things.
The premium (what you pay) is the rate or risk calculation, with any discounts, including no claims discount, applied.
So in the example of car insurance, an accident will increase the base calculation of your 'insurance' rate or risk.
Any discounts, no claims or otherwise, are then applied to the amount calculated.
Example:
Insurance before accident with NCD
= £200 (your risk calculation) - 40% of £200 no claims discount
= £200 - £80 = £120 to pay
Insurance after accident with protected NCD
= £400 (your increased risk calculation) - 40% of £400 protected no claims discount
= £400 - £160 = £240 to pay
Insurance after accident without protected NCD
= £400 (your increased risk calculation) - 0% of £400 no claims discount
= £400 - £0 = £400 to pay
Protected no claims discount protects the percentage of discount applied to the base risk calculation and is not protection from an increased basic risk calculation and hence increased cost of cover.
Hope this helps in understanding.
More info
http://www.confused.com/car-insurance/guides/how-car-insurance-is-calculated