Liability: You get into an accident with another vehicle where you are deemed "at fault," the insurance company will pay for the other parties damages, but you will have to pay for your own car and/or hospital bills.
Collision: If you get an accident where you are deemed "at fault," the insurance company will pay for the other parties' damages and your own.
Comprehensive: The insurance company will pay for any damage done to your vehicle due to theft, act of God, vandalism, etc.
Edit: By the way, if you get into an accident where the OTHER person is at fault, their insurance company will pay for your damages. Your company isn't involved at all. If the other party is at fault, but he doesn't have insurance, your insurance company may or may not cover your damages. This depends on the type of policy you've opened up.