Since you do not own the building of which you live, if there is a loss, the building insurance policy only protects the property owner and rarely will it afford coverage to the tenants in the building. To protect yourself, renters insurance provides coverage for your personal effects and liability protection.
Renters insurance is relatively inexpensive. The first part of renters insurance is for the value of your personal items in the apartment. This would include clothes and furniture. The second part of the policy is liability, which would protect you if you are accused of negligence to another person.
Please note that renters insurance does not provide coverage for roommates. It is specific to the named person on the policy.