Plain version: insurance is a promise to make someone whole if something uncertain goes wrong. A store owner does not know whether a windstorm will tear off the roof this year. An insurer agrees to pay that loss if it happens.
California's legal definition (Ins. Code §22): insurance is a contract whereby one undertakes to indemnify another against loss, damage, or liability arising from a contingent or unknown event. The two key ideas are indemnity (paying back a loss) and uncertainty.
Insurance: paying a store's windstorm damage, or paying a driver's legal liability after she injures a pedestrian.
Not insurance: painting a house on a set date for a set price, or paying a fixed sum on a chosen date no matter what happens. Nothing is uncertain and nobody is indemnified.
What may be insured (§250): any contingent or unknown event, whether past or future, that may damnify a person who has an insurable interest, or create a liability against him. So both property losses and liabilities can be insured.
The word past surprises people. Title insurance covers an unknown past event: a lien on the land may already exist when the policy is bought, but nobody knows about it until later.
The limit: §250 opens with except as provided in this article, and §251 in that same article bars insuring a lottery or its outcome.