A Mehmet Oz, MD. Cardiology (Cardiovascular Disease), answered
Indemnity plans are the oldest and most liberal type of health insurance plan—the one your dad may have had when he wore the gray flannel suit to his job in the 1950s. Even up to the 1970s, most Americans still had indemnity plans (also called fee-for-service plans).
Your parents (and their employer) paid a lot for this plan, but they may not have complained too much because (1) there was no other choice, and (2) the coverage was wide and largely unrestricted. They could see any doctor, anywhere, and get any medical service they wanted. After paying a deductible (today, it may be $500 to $2,000 annually)
they would pay a portion (say, 20%) for every service they got, from a blood test to baby delivery.
Today, about 1 in 10 Americans with employer-paid health insurance have some version of an indemnity plan. These policies are fairly expensive because the insurers don't require members to use specific hospitals or doctors, so they often get no discount for services (insurers who limit their members to "in-network" hospitals and doctors can negotiate huge discounts with those providers because they're guaranteeing them a steady supply of business).
Indemnity plans can be the best choice for people who want ultimate freedom and are willing to pay the higher premiums and co-payments and don't mind dealing with extra paperwork.