What is Liability Insurance? Liability insurance is the coverage that would protect if you caused an accident that injured someone else or caused damage to their property. Auto liability insurance is broken down into bodily injury coverage and property damage coverage. What Does Liability Insurance Cover? Imagine you are driving down a residential road and don’t realize there is a stop sign ahead. You try to hit the brakes to stop before you get through the intersection, but wind up hitting a car in front of you as well as the fence of the house on the corner.