Admitted insurance companies are those in the United States that have been admitted or licensed by the state licensing agency. The insurance they sell is called admitted insurance. Non-admitted companies have not been approved by the state licensing agency, but are allowed to sell insurance under special circumstances when they meet an insurance need that admitted companies cannot or will not meet.
Comprehensive car insurance covers damages from an "act of God," or events that are not caused by a car driving into something else. An "act of God" can include things like damage from a heavy tree branch falling on your car. Since you have no control over when or why a tree branch would fall on your car, this kind of accident would be covered under your comprehensive policy.