Bodily Injury covers if you are involved in an accident and cause injury to another party. The coverage can be listed as split limits or a combined single limit. For example: If your limit is $100,000/$300,000 on your declarations page, you are covered for up to $100,000 per person and up to $300,000 per accident. If you are sued by someone because of an accident, this is the coverage that would typically come into play.

Property Damage covers any damage that you cause to another person's property. This could be another vehicle, a road sign you it, or even you ran into a building (it happens).

Medical payments covers if you are injured in an auto accident and have medical bills as a result of that accident.

If you are struck by a vehicle that either has no coverage or they have limits lower than your uninsured/underinsured limits, then you could claim for bodily injury benefits under your policy. 

Comprehensive, also known as "other than collision coverage" provides coverage for damage to your vehicle if it is physically damage by something other than a collision. This could be anything from a tree branch falling on your vehicle, hail damage, if you hit a deer, or even theft of the vehicle. 

Collision will cover if your vehicle collides with another vehicle or stationary object.

Many companies offer other additional optional coverages to protect you in case you are involved in a loss. These can include coverage for a rental vehicle while your vehicle is being repaired, roadside assistance, or loan/lease GAP coverage.