Auto insurance is comprised of two primary categories of coverage: Liability and Physical damage. There are many other coverages available such as Uninsured Motorist, Personal Injury Protection, Medical, Towing, Lease Gap, etc., but in broad terms Liability and Physical damage are most common coverages purchased.
Liability coverage is mandatory in most states and is used to pay for Bodily Injury and Property damage to others caused by your negligence.
Physical damage coverage is insurance that you purchase within your policy to pay for repairs to damage to your vehicle. The two physical damage coverage categories are Comprehensive (or Other than Collision) and Collision.
A simple way to understand which coverage applies to damage to your vehicle is this: If the damage is from something that is out of your control it is likely a Comprehensive loss. If it is the result of your actions, then it is likely a Collision loss.
Examples of Comprehensive losses are striking an animal, broken glass, vandalism to your vehicle, theft of your vehicle, something falling from the sky, etc.
Collision examples include driving through a pothole, striking an object or other vehicle or being struck by another vehicle (whether the other party has liability insurance is another matter).
Your policy would normally have a deductible described on the declarations page that would apply to each loss. Your insurance company would then pay the balance of the repair costs.
Typically comprehensive losses do not have a negative effect on your insurance premiums. Collision losses, especially At-fault accidents, will normally result in an increase to your premium at policy renewal.