Most regular homeowners or landlord policies will not cover incidents that occur during a short-term rental or Airbnb stay.
You'd be smart to buy insurance that specializes in short-term rentals and Airbnb. As of June 2017, there were few insurance options out there specializing in this market.
Proper Insurance is underwritten by Lloyd's of London and operates like a conventional insurance model. Pay a monthly premium. Enjoy stress-free coverage. Their customer service is responsive and their coverage areas are strong. They offer a great product.
Slice has a slightly different model, offering on-demand insurance for each stay instead of an annual policy. Their coverage areas are broader than most carriers. (For instance, they cover you for liability should your guests get drunk at your house and then drink and drive and injure someone.)
It takes one dumb guest to wipe out all your short-term rental profits … and maybe all your savings. So be sure you're covering yourself properly