Most tenants think renters insurance is a formality their landlord imposes to protect the building. It is close to the opposite. The building is already insured, and none of that insurance covers you.
What it covers
Your belongings, against fire, theft, water damage and the rest. Add up a laptop, a bicycle, a wardrobe and a kitchen and the number is usually far higher than people guess.
Personal liability. The important one. If your overflowing bath damages three units below you, the building's insurer pays for the repairs and then comes after you for the money. Liability coverage is what stands between you and that bill.
Additional living expenses. If the unit becomes uninhabitable, this pays for somewhere to stay while it is repaired.
A policy with $1 million or $2 million in liability coverage typically runs $15 to $30 a month. The subrogated claim it protects you from routinely runs into six figures. It is the cheapest genuinely useful insurance most people will ever buy.
Why your landlord asks for it
Because their insurer told them to. A tenant with liability coverage is a tenant whose accident does not become the landlord's loss, or the landlord's deductible, or a claim on their record. It is entirely reasonable, and a lease term requiring it is enforceable.
The structure, which is the landlord's responsibility. Flood and sewer backup, usually available only as an add-on and worth having in a basement unit. Anything you failed to declare, and high-value items such as jewellery or instruments beyond a low sub-limit unless separately scheduled.
Some buildings and some units cost noticeably more to insure. It is a small number in the monthly budget, and it is better known before you commit than after.