Subrogation is a complement of indemnity. Subrogation provides the insurer with the benefit of recovering from the insured anything he received by third parties for the loss. Subrogation also provides the insurer with the ability to sue in the name of the insured against those who caused the loss.
The insurer has a right of subrogation when (1) the insurance policy is indemnity insurance, (2) the insurer has made payment under the policy, and (3) the policy does not exclude the right of subrogation.
Note that excluding the right of subrogation will lead to a higher premium by the insured.