One of the priciples of insurance is UBERRIMA FIDES - Perfect good faith; abundant good faith.
It means the policy holder most act in utmost good faith, and that the Insurer will provide cover on the basis of the proposal.
Now if anything that might change the nature of the risk happens it's up to the insured to inform the insurer.
A "material" fact is one that might alter the opinion of the underwriter as to the risk itself, and the premium to cover it.
Failure to disclose a material fact can make a claim voidable or totally invalidate the contract.
In motor insurance common examples are:-
1/. Named drivers. Parents insure car in their names with children as named drivers. The proposal form will ask "will you (proposer) be the main driver?" If the parent doesn't tell the truth in answering this question the cover may be in jeopardy.
2/. Modifications. Big business this, and dangerous too from an insurance view point. If a car has it's standard specification altered in any "material" way, the insurer should be informed so that it can reconsider the revised risk.
Material alterations might be increasing the engine power, lowering the suspension, fitting racing seats, or a rollcage, etc.
Other mods. which are routinely ignored are fitting a big aftermarket stereo, oversized alloy wheels and fat tyres, or a bodykit. It could be argued that these are only cosmetic, but that'd be incorrect because the chances of theft will have increased, as the car will be of more value to a prospective thief.