If after an insurance claim is paid out by your insurance company, it is deemed that another party was actually the negligent one, then your insurance company (via the insurance policy contract) has the right to go after the negligent party. This right is usually found in the "Conditions" section of your insurance policy. This conditional right can, however, be waived. This means that your insurance company would then not be allowed to go after the negligent party. The term for this waiving of rights is called Wavier of Subrogation.
Often you will see the Waiver of Subrogation in commercial leases. Landlords will require that tenants have this verbiage in their insurance policy so that if a claim occurs at the leased location that the tenant's insurance company cannot come back after them for damages. The landlord, however, would be less inclined to have this wording on their policy since it would mean they and their insurance company would not be allowed to go after their tenant after a claim. A building owner and their insurance company usually have more to lose (the building and its rental income) than the tenant does so they would be very interested in being able to go back after a negligent party.
There are two example of where a landlord may want the Waiver of Subrogation wording on their own insurance policy. The first is if they are renting to a family member or friend who they know doesn't either have enough assets or money to be able to cover them in case of a claim, they may not want their insurance company to be able to go after them to collect for damages. The second is if the landlord and tenant are owned by the same person or organization. In some cases, usually for legal or tax reasons, a person may have one company that owns the building and another company that owns the business that is the tenant. In those cases you would probably want both the landlord and tenant policy to have a Waiver of Subrogation clause in their policies so that you don't have your two insurance companies fighting over payout.
Another place where you will see Wavier of Subrogation is in situations where companies or organizations will subcontract work to other companies or organizations. Often, if a business is going to hire another business to do work on their behalf they will request that the subcontractor have Wavier of Subrogation on their policy. Similar to the Landlord/Tenant relationship, if the contractor requires the subcontractor to have Waiver of Subrogation on their policy it means the subcontractor, if a claim arises, is not able to go back after the contractor for money.
When entering into a lease or a business contract it is important to know if you are going to be required to have Waiver of Subrogation and if you have it or not in your insurance policy. It is best to have both your legal team and your insurance professionals review contracts to make sure you are adequately protected.