Renters Insurance is like homeowners insurance for renters. Some apartment complexes in town require tenants to carry a renters insurance policy, but don't despair—it's pretty cheap. Many (most? all?) auto insurance companies give hefty discounts on your auto policy if you pick up a second policy—homeowners, renters, whatever. You may even end up with net savings, actually saving more on your auto policy than you pay for your renters policy (State Farm Insurance example: with a two-car policy, a base-line $80/yr. renters policy knocked more than $100/yr. off one of the car policies).
Renters insurance is different from homeowners' insurance in a few ways. Policies usually cover damage to your personal belongings and liability for injury in your rental property. The policy doesn't cover damage to the building itself—your landlord should have a policy for that. If, however, you're responsible for a fire, explosion, or similar loss to the building, the liability coverage on your renters insurance can respond to that. Without that coverage, you'd be responsible for the owner's deductible (potentially tens of thousands of dollars), along with losses of other affected residents. Liability protects you by defending you if another tenant sues you or their insurance subrogates against you for the loss you're responsible for, as well.
Policies also cover "loss of use," or the additional living expenses incurred after a covered loss such as a fire. According to California renters insurance provider Effective Coverage, a renters insurance policy in Davis will average between fifteen and eighteen dollars a month.