Liability insurance protects you in the event that someone claims that your business caused them to incur some type of damage or harm. Your liability insurance pays for such damages to third parties resulting from bodily injury or property damage for which your business is legally liable, up to the policy limits, as well as legal & defense fees. It also covers the medical bills of any people injured by your business.
Property insurance can be added to your Liability policy to help you replace the building used by your business when it is damaged by fire/wind or other covered losses. Property insurance can also cover your business personal property/contents/inventory from losses.