Do not assume that the landlord's insurance covers your personal belongings, because more than likely it does not. Your landlord probably has insurance that covers the building only.
Renters insurance covers personal belongings for their actual cash value at the time of the loss.
However, there is limited coverage for furs, jewelry, monies, fine arts and other specific valuables. These special items may be covered under a special addition to your renters policy or under a separate policy. Your renters insurance will also pay for any increase in living expenses when your residence can not be occupied because of damage caused by events previously listed. For example the policy would help in paying for a hotel and food in restaurants while you are out of the apartment or unit that is being repaired. It includes coverage of legal fees in the event you are sued.