The technical definition of "indemnity" means to make whole again. There are two types of insurance contracts;
1. an "indemnity" policy and
2. a "pay on behalf" or "on behalf of" policy.
The difference is significant on paper, but rarely material in practice.
An "indemnity" policy will never pay claims until the insured has paid out of pocket to some third party; for example, a visitor to your home slips on a floor that you left wet and sues you for $10,000 and wins. Under an "indemnity" policy the homeowner would have to come up with the $10,000 to pay for the visitor's fall and then would be "indemnified" by the insurance carrier for the out of pocket costs (the $10,000).
Under the same situation, a "pay on behalf" policy, the insurance carrier would pay the claim and the insured (the homeowner) would not be out of pocket for anything. Most modern liability insurance is written on the basis of "pay on behalf" language.

When insured parties experience a loss for a specified peril, the coverage entitles the policyholder to make a 'claim' against the insurer for the covered amount of loss as specified by the policy. The fee paid by the insured to the insurer for assuming the risk is called the 'premium'. Insurance premiums from many insureds are used to fund accounts reserved for later payment of claims—in theory for a relatively few claimants—and for overhead costs. So long as an insurer maintains adequate funds set aside for anticipated losses (i.e., reserves), the remaining margin is an insurer's profit.