What's happened is that we've essentially handed over our health care to big corporations. It works in the sense that it's cheaper than paying the going rate at the hospital, so we "save money", but I'd say it's not really a good thing.
What happens is that first you choose a plan- the basic (and cheapest) plans might be fore emergency care only, meaning if you're on the brink of dying and need to go to the emergency room, you'll be covered. Regular doctors visits will probably not be part of that, ranging all the way up to the most expensive plans only having to pay a small copay (flat fee) for your regular visits, and less than ten percent of your hospital bill should you need it, plus a discount on gym memberships, and dental and vision care as well. Not every company covers the same drugs, not every company covers the same treatments.
With the recent Affordable Care Act, lower income citizens can get a government paid discount on insurance plans that meet certain standards. Unfortunately if you're poor, they are sometimes still unaffordable at that point. You may be able to qualify for a government program called Medicaid if you cannot afford regular insurance even with the discounts.
Not everything is covered unfortunately- Most plans will only cover treatments, tests, and procedures that are deemed either medically necessary, or preventative. Things like boob jobs and tummy tucks are most certainly not medically necessary except in very specific circumstances. Often times your doctor will have to submit paperwork to have the procedures approved before the insurance companies will pay for it. Going to see a specialist often times requires a referral from your normal doctor, so... you might have to have two appointments, depending on how much of a stickler your doctor is.
Medications are covered- not everything though. I know with Medicare (government insurance program designed to help with healthcare costs for senior citizens and disabled people who are unable to work) that they are only required to cover one drug from each class of drugs, rather than a range. Depending on your plan, you may have to either pay a flat fee or a percentage of the cost at your pharmacy. Generic drugs will generally be cheaper- usually around $5 for a 30 day supply. Name brand drugs? Sky is the limit on that one. Depending on how new it is, and how specialized it is, they can cost anywhere from $15 for a 30 day supply to well over $5000. Things for life threatening conditions like HIV medications and stuff for transplant recipients are often times significantly higher.
If you can afford it, insurance can be really nice in America- you've got a team of people that go to bat for you with health care issues, and such. If not, it's a neverending nightmare of authorizations and bills and technicalities. Even with recent legislation to reduce the cost of insurance, a lot of people still can't really afford health care. I know quite a few people that just straight go without, and negotiate a discount with the hospital if anything does require them to go to the hospital. The ugly side to that is a lot of people trying to tough out injuries, going to work when they really need to be resting, and suffering needlessly. We are in desperate need of reform, but getting the big ole corporations to release their stranglehold on the golden goose of health care is a pretty nasty challenge in and of itself.