Waiver of subrogation is when one party (usually an insurance company) gives up the right to recover a paid loss against another party in the event a loss occurs. In order to fully understand what Waiver of Subrogation is, let's look at the parts.
Waiver – Abandoning, surrendering, or relinquishing rights a party is legally entitled to, either by contract or law.
Subrogation – Is an assignment to an insurance company (insurer) in the insureds (you or your company) name either by policy terms or by statute (law), to recover money paid from the insurance company towards a claim. Common subrogated assignments come from property damage, but other losses can invoke subrogation that include indemnity (making whole) policies. An example of an insurance policy where subrogation doesn't occur is in life insurance policies. If your spouse dies because of negligence of another, the insured (you and possibly others) maintain their right to sue the negligent party for the death.
Putting it all together, a waiver of subrogation in an insurance policy is an insurance company releasing another party from fear that if there's a loss, the insurance company may come after them. It's often done via endorsement(s) to an existing or newly issued policy, but it can be in the policy language to begin with.
Using the death of a spouse example again, if you have auto insurance and life insurance on your vehicles and family members and your spouse is killed by another motorist who is at fault, your auto insurance company can go after the "at fault" party to recover money paid to you to reimburse you, but your insurance company can't.
Subrogation is one tool insurance companies use to keep insurance premium lower. It's because the insurance company knows or at least believes some of its losses are recoverable from the negligent parties. When an insurance company grants a waiver of subrogation, it must rely solely on insurance premiums to pay losses/claims, so insurance companies will either charge more for the policy or charge for a waiver of subrogation endorsement to an insurance policy.