Loss damage waiver is an agreement with an auto rental company in which the renter is released from liability for physical damage to the vehicle in exchange for a fee, subject to the terms of the rental agreement or a state statute if one exists.
It is not insurance but a contractual obligation subject to many restrictions. In some contracts, the renter may be able to choose either a full damage waiver or one that holds the renter responsible for damage only over a certain specified amount, sort of an inverse deductible. The rental agreement typically stipulates that purchasing the damage waiver is not mandatory.