Most personal auto policies extend whatever coverage you have on your own vehicle to a short-term rental vehicle if the rental vehicle is a private passenger car, pickup truck, van or trailer. However, with regard to damage to the rental auto, the rental car company might be able to charge fees for losses or damages to the vehicle that might not be covered by your insurance policy, such as loss of use when the auto is withdrawn from service for repair, or diminished value upon resell. Therefore, it is often a wise idea to purchase the rental company's "collision damage waiver" (CDW).
If you do not have your own insurance, many car rental liability policies cover you, but usually only at the state's required minimum, which are usually extremely low limits. Also, you should buy the collision and comprehensive coverage offered by the rental company for your own protection.
A CDW simply releases you from financial responsibility if you damage the vehicle you are renting, provided you comply with the terms of the rental contract. The terms of CDW's can vary considerably, and CDW's are not state-regulated, which means they are technically not insurance.
It's always a good idea to review your policy before renting a vehicle and, if necessary, call your agent.