An indemnity is a sum paid by A to B by way of compensation

Damages

In law, damages is an award, typically of money, to be paid to a person as compensation for loss or injury; grammatically, it is a singular noun, not plural.- Compensatory damages :...

 for a particular loss suffered by B. The indemnitor (A) may or may not be responsible for the loss suffered by the indemnitee (B). Forms of indemnity include cash payments, repairs, replacement, and reinstatement.
Indemnity is often used as a synonym for compensation

Damages

In law, damages is an award, typically of money, to be paid to a person as compensation for loss or injury; grammatically, it is a singular noun, not plural.- Compensatory damages :...

 or reparation

Reparation (legal)

In jurisprudence, reparation is replenishment of a previously inflicted loss by the criminal to the victim. Monetary restitution is a common form of reparation...

. While it is true, that 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.