Wow..I bet that policy is inexpensive. It means that the first $3,500 of medical expenses each year come out of your pocket. After that, the insurance company will pay 50% of your medical bills - if you have a $100 office visit, they pay $50. You also might want to check if they pay 50% of the full amount or if they use a usual and customary schedule meaning that if the UAC for an office visit is $70 and the doctor charges $100, they pay $35 (50% of the UAC of $70) and you would pay $65 ($100 for the office visit minus the $35 the insurance pays).
You pay the first $3500 of medical bills and half of the rest.
For example, if there are $10,000 of medical bills, then you pay $3500 plus 1/2 of the other $6500 for a total of $8250, and the insurance company also pays 1/2 of $6500, which is $3250.