The finance company for a non-leased vehicle usually requires physical damage coverage. It will cover any damage to their asset (the vehicle).

An explanation of that coverage can be found on our Coverage Definition page.

Comprehensive Physical Damage Coverage Covers your vehicle, and sometimes other vehicles you may be driving for losses resulting from incidents other than collision.

For example, comprehensive insurance covers damage to your car if it is stolen; or damaged by flood, fire, or animals. Pays to fix your vehicle less the deductible you choose. To keep your premiums low, select as high a deductible as you feel comfortable paying out of pocket. Coverage is limited to the terms and conditions contained in the policy.

Collision Coverage Covers damage to your car when your car hits, or is hit by, another vehicle, or other object. Pays to fix your vehicle less the deductible you choose. To keep your premiums low, select as large a deductible as you feel comfortable paying out of pocket. For older cars, consider dropping this coverage, since coverage is normally limited to the cash value of your car. Coverage is limited to the terms and conditions contained in the policy.

In addition to Physical Damage coverage you will need Property Damage Liability and PIP to satisfy the state requirements. 

You will need to select limits for your Property Damage Liability and Bodily Injury Liability. A Limit is the maximum amount of insurance the insurance company will pay for a particular loss, or for a loss during a period of time.

You may select a deductible for PIP and your Physical Damage. A Deductible is a dollar amount the insured must pay on each loss to which the deductible applies. The insurance company pays the remainder of each covered loss up to the policy limits.

You should select the deductibles and limits that you can afford. Read our article, How Much Car Insurance Should You Buy?