Notice that liability insurance only covers damage you may do to other people or their property.
If someone else is found legally liable for damage to your vehicle or yourself, their liability insurance will pay for those damages (up to the limit of their policy).
But what about damage to your own vehicle due to an accident that you cause, or due to circumstances outside of your control (such as fire, flood, theft, etc.)?
This is where Collision and Comprehensive insurance come into play.
Driving a vehicle creates a risk of damage to your own vehicle in a collision.
If someone else is found legally responsible for the accident, they and/or their insurance must pay to repair the damage to your vehicle.
But if you are involved in an accident, and nobody else is found legally responsible, you'll either have to live with the damage to your vehicle or pay to have it repaired.
Collision Insurance covers the costs to return your vehicle to its pre-collision condition, and is optional throughout the United States.
Owning a vehicle creates a risk of damage to your own vehicle by a number of non-collision perils.
These perils are (mostly) things that could happen to the vehicle when it's parked.
Comprehensive Insurance covers the costs to return your vehicle to its pre-event condition in the events of:
Natural disasters (floods, hurricanes, tornados, earthquakes, volcanic eruptions)
Riots and vandalism
Theft of all or part of the vehicle
Fallen objects (hail, trees, branches, projectiles, etc.)
Contact with animals (see *Nerd Note below)
Comprehensive coverage is optional throughout the United States.
*Nerd Note: Even though hitting an animal seems like it should be a collision risk, insurance companies treat it as a comprehensive risk, for a very good reason. Collision claims cause a driver's insurance rates to increase more than comprehensive claims. Swerving to avoid a deer because your rates will go up and flipping your car as a result is more costly for everybody, so insurance companies classify animal contact as a comprehensive risk to avoid creating the wrong incentives.