A material fact is any fact that would reasonably influence an insurers underwriting decision on a policy, i.e.: would influence their decision whether to issue a policy or the premium for the policy.
For example, if you apply for an automobile insurance policy and represent that you are accident and violation free, when in fact you were responsible for a DUI accident last year, your misrepresentation is considered material as the insurer would not have issued the policy if in possession of the facts.
Conversely, if you insure a 2009 F-150 Black pickup truck when the vehicle is , in fact, a 2009 F-150 Green pickup, the misrepresentation is not material as it would not influence the decision to insure or the premium charged.
The effect of a material misrepresentation varies by state. In the majority of states, known as increase in risk states, a material misrepresentation is grounds for recission of the policy, i.e.: the policy is declared void ab initio (from the beginning) effectively no policy ever existed and any intervening losses are uninsured. In a minority of states, known as contribute to risk states, the misrepresentation must actually contribute to a loss for the loss not to be covered, e.g.: you represent that a wood framed & sided building is fire resistant masonry construction and the building burns to the ground.
Life insurance is treated similarly with the exception that policies are required to contain incontestability clauses which prevent recission after the passage of a period of time (typically two years).