Ah. It's paying someone to make good your future losses.

You save money if you suffer a loss before the amount you've paid into the contract would suffice to replace that loss. They make money by asking for payments in an amount that they will receive more from customers than they expect to pay for losses across a large number of customers.

Needless to say many a greedy or desperate person has purchased an insurance contract and then arranged for the destruction of the thing insured.