Tenant Insurance covers your liability if the common elements or property of other owners are damaged because of your oversight. For example, you forgot to turn off the tap and water flooded, as a result the floor is damaged and furniture of your downstairs neighbor is affected. Most of the buildings only recommend tenants to buy this kind of Insurance, and many tenants opt out. It is also possible that your build requires every tenant to buy it, in that case you don't have other choices unless you are able to negotiate individual lease terms.