Liability insurance is included, collision damage insurance is at an additional charge. Sometimes full collision is half as much as the rent itself. There is still a deductible involved, unless you buy Island Car's "zero liability" coverage which costs $30 a day on top of the rental fee: http://www.islandcarrentals.com/Home.aspx/AutoCoverageOne would think when you rent a car, part of the rent is insurance
Insurance works the same way with rental cars in the US - CDW is around $10-25 a day, but many credit cards include that insurance if you use their card to rent - not so in Jamaica with 99.9% of credit cards. Very few will cover collision in Jamaica (or Ireland or Israel or Iceland, for some reason).