The term for the amount paid by an individual before insurance kicks in is known as the deductible. This is part of the cost-sharing structure of an insurance plan, along with co-payments and co-insurance, to mitigate moral hazard by having the insured bear some expenses.
For traditional insurance, a certain amount of money each year that is paid by you before the insurance payments begin is known as the deductible. This is the fixed amount that the policyholder must pay out-of-pocket before the insurance company starts covering costs. After the deductible is met, you may also incur co-payments or co-insurance payments, where you pay either a fixed fee for a service or a percentage of the costs, respectively.