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.
The big reason that D.C. makes the cut is population density. The entire district is basically an urban area, which leads to higher insurance rates. According to Census information, D.C has a population density of 11,020 people per square mile. While this number is certainly smaller than New York City, which clocks in at 28,256 people, it puts it well above other large cities, such as Houston and even Los Angeles.
Collision coverage has a deductible, which is the amount you pay before your coverage helps pay for your claim. You can typically choose the amount of your deductible when you buy coverage. So, if you choose a $1,000 deductible and your car is later damaged in a covered accident, you'd have to pay $1,000 toward repair costs. Your collision coverage would help pay the rest, up to your coverage limit.