Comprehensive insurance is commonly confused with collision. They both insure your car but cover different events. Collision covers car accidents, and comprehensive covers events out of your control. Think of it like this: Collision is colliding with something else (other than animals). Comprehensive is basically all other events. Accidents with animals are covered by comprehensive (and not collision) because these accidents are considered out of your control.
If you have paid off your car, comprehensive coverage is optional. It may be a good idea to find out the Kelley Blue Book value of your vehicle. Would you be able to pay that amount to repair or replace your vehicle if it were stolen or damaged in an accident? If you can't afford to pay much out of pocket, then buying optional coverages, like comprehensive coverage and collision coverage, may be a smart investment.