If you do a dangerous activity, then you get some sort of insurance. (At least, I think you do, I'm a bit young to know when insurance is used, but my aikedo sensei is insured.)
Your Aikido sensei has insurance that covers all of the students and the building.
Insurance pays out in case of incident. If I have car insurance (and I'm legally forced to buy it if I want to drive,) I pay it monthly, but they only pay if something happens that is covered by the insurance. If I get into a car crash, they'll pay for a certain amount of repairs based on how much I pay a month. If I cause injury to someone in the crash, I hit a pedestrian for example, they pay for their injuries up to a certain amount (minimum personal injury coverage for my state is $1M,) and jack up my monthly pay rate (called the premium) and make me pay the rest. My home insurance pays out if my house burns down (and it's not caused by me setting it on fire on purpose.) Health insurance pays out if you stay in the hospital because you're injured or extremely sick.
I don't have health insurance because it would cost more than all of my weekly pay and for whatever reason I don't qualify for Medicare/Medicaid, despite being extremely low income. One of the DHS workers heavily implied that I would never qualify because I have external genitalia and/or not enough melanin in my skin.