When you purchase car insurance you are purchasing both first party coverage, which covers you and your property, and third party coverage, which covers other people involved in the auto accident (either in your vehicle or other vehicles in the crash).
Different types of coverage can be purchased. Comprehensive coverage covers your vehicle in the event of fire, theft, vandalism, and acts of nature. Collision coverage covers your vehicle in the event of an auto accident.
When you have been involved in car accident, your insurance company will require that you contact them in a timely matter. If you do not report an auto accident to your insurance company, they can attempt to deny coverage for the accident.