Your landlord insures the building. They do not insure your belongings, and their policy will not help you if your possessions are damaged.
Buildings vs contents
Buildings cover is the landlord's. Contents cover is yours – furniture, electronics, clothing, jewellery.
Tenant liability
Often the most valuable part for a renter. If you cause damage to the property – a burst washing machine hose, a fire – you can be liable, and the sums are not small.
Valuables
High-value single items usually need to be listed separately. Check the single-article limit before assuming your watch is covered.