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The AMA is a not-for-profit organization chartered to promote/educate about model aviation. They do this in a number of ways you can find on their website. As one of the benefits you receive insurance coverage (secondary if you are covered by a policy such as your homeowners, or primary if you have no other insurance) which helps protect if your FREE FLIGHT, control line, or R/C aircraft causes personal injury or property damage. Having this insurance/membership allows you to fly at an AMA Chartered club!
Check out the website, find a local member to go talk to, and if you find you like what it has to offer join!