Subrogation is the right of an insurer to seek reimbursement for money paid on a claim, from the responsibile party.
It is commonly seen when a person is injured in a collision, and that person's health insurance pays for medical treatment. The law gives that health insurer the right to get its money back from the person that caused the injury. Medicare and Medicaid also have statutory rights of subrogation.
Your uninsured motorist insurance carrier, has a contractual right to subrogate for benefits it pays out. These "subrogation interests" must be dealt with in the process of resolving your case. You may need to obtain a waiver of subrogation from your UM carrier, before you accept the liability insurance policy limits from the responsible party. Failing to obtain a waiver of subrogation can bar your claim for UM benefits under your own insurance policy.