An insurance term in which one party (the insurer) assumes the legal rights of another party (the insured) for whom a debt has been paid.  This gives the insurance company the right to sue the third-party that caused the damages in order to recover some or all of its costs.  Some leases will call for a mutual waiver of subrogation, meaning that the insurers for both parties will waive the right to sue the third-party who caused the damage.