It means they won't pay in full for repairs that put the car in a better state than before the failure, so you would have to contribute to the cost of such if needed.  Visiting from DISCO3.CO.UK
2006 Discovery 3 TDV6 Auto HSE Zambezi Silver

the betterment clause = after the repairs the car will be in a better condition, so you will have to pay a contribution in percentage terms towards parts only depending on vehicle mileage/age, labor and diagnostics costs are paid out in full.