Which term refers to the amount of money you must pay each year cover your medical expenses before insurance policy starts paying?

The term you are looking for is 'deductible'. A deductible is the amount of money that an insured person must pay out of pocket for covered medical expenses before their insurance company begins to pay for those expenses. Deductibles are typically a set dollar amount, such as $1,000 or $2,000, but they can also be a percentage of the total medical expenses, such as 10% or 20%.