Indemnity is often used as a synonym for compensation or reparation
In general insurance pays indemnity: Indemnity is often used as a synonym for compensation or reparation. All three can be construed as obligations to act on an injured party's behalf given the occurrence of a contractually-specified event. However, indemnity as a legal concept has a much broader meaning than the other two terms; namely, an indemnity is to make a party to a contract "whole" again should that contractually-specified event occur.
While the event may be specified by the contract, the actions that must be taken to make the injured party "whole" again are largely fact-based and unknown to the parties until the event occurs, while the maximum liability is often expressly limited by the contract.
A car insurance policy is an example of indemnification. If a purchaser of car insurance policy is involved in an accident wherein the liability for the accident is undisputedly of their insured driver, then the insurance carrier has the duty to indemnify their insured driver in very specific ways to make them "whole" again.
An insurance carrier may pay compensation (recompense for lost wages that would have normally occurred), pay them for medical/legal/(pain and suffering) damages (i.e., those costs arising specifically as the result of the accident), reparations to tow and repair the vehicles involved in the accident returning them to their original condition, and the payment of rental vehicles while awaiting repairs.
Breadth of the insurance carrier's obligations
It is in the breadth of the insurance carrier's obligations that we see the application of an indemnity; in other words, an indemnity is a "generalized promise of protection against a specific type of event by way of making the injured party whole again."