Renters insurance is meant to cover your personal belongings and liability if damage to the landlord's asset is found to be your fault.
Let's say you leave the water running in your tub and you flood your apartment. Renter's insurance will pay for any of your personal furniture, clothing or electronics that are damaged in the flood.
But it will also pay to replace the damaged floor coverings and if the flood causes any mold or damage to the walls as well. Some policies will also pay for a hotel room or relocation costs if the apartment cannot be lived in due to the damages. It will also cover your liability for damages that may occur to your neighbors apartment/belongings.
Renter's insurance also covers personal belongings in your vehicle if it is broken into. Your auto insurance won't cover things like sunglasses, cd's and iPods.
If you don't have renters insurance in this situation, the landlords insurance company is within their rights to come after you for reimbursement for damages.
And the landlords policy won't pay to replace your personal belongings. A flood like the one I mentioned above can cost anywhere from a couple of hundred dollars to thousands of dollars.