Something that's insured is protected by an insurance policy — in other words, its loss or damage will be compensated by an insurance company. If your laptop is insured, you'll get enough money to replace it if it's stolen.
If an insured house burns down or is damaged in a storm, an insurance company will pay to repair or replace it. In exchange, the homeowner pays monthly (or sometimes annual) fees. If you have a life insurance policy or insurance that covers your health care, you are also insured. Insured, by way of the verb insure, comes from the original ensure, which has the roots en-, "make," and sure, "safe, strong, or resolute."