Home is where you make your life, and approximately 1/3 of all households in the United States are rented. One thing to remember is that the landlord, or owner of that home, likely has that building insured, but this does NOT extend to your stuff contained within. Therefore, it becomes your own responsibility to obtain insurance to protect your personal property in the event of a disaster.
Renter's insurance covers your contents on a replacement cost basis and will replace or reimburse you for their loss or damage. All this with the exception of the building you are renting. These policies have two distinct sections:
Property Coverage: Covers any personal belongings, but does not cover the building you live in.
Liability: Covers unintended damage to your rental or accidents that may occur at home.