Renters insurance
A policy that protects a renter's own belongings and covers you if you're found legally responsible for someone else's injury or property damage. Your landlord's insurance covers the building's structure, not your things.
New Jersey example
A kitchen fire in your New Brunswick apartment ruins your furniture, and you stay in a hotel while it's repaired. Renters insurance can pay for your damaged belongings (Coverage C) and your extra living costs (Coverage D), minus your deductible. It does not cover flooding. Flood insurance is available through the National Flood Insurance Program.
Official source
A Consumer Guide to Renters Insurance (NJ Department of Banking and Insurance)
This is a plain-English summary. Rules and dollar amounts change, so check the official source or a professional before you file or sign anything.