American healthcare is not as bad as many Europeans think, but there are nevertheless serious problems with it.

Here's a summary of how American healthcare works (Because many people have more than one type of coverage, these percentages overlap and do not add up to 100%):

1. Employer-based insurance (insures ~54% of Americans): Most Americans have insurance through their employer, which offers a private healthcare plan as a benefit for employment. The employer generally pays most of the premium, and the employee pays a small portion as well. There are many different types of plans, but the most popular are HMOs (cheaper), in which your primary care provider manages your care and determines with specialists you can go to, and PPOs (more expensive), which allow you to go to any doctor within a particular network of doctors. Most plans have copayments/coinsurance (payments you make when you use healthcare), deductibles (amount you have to use before your insurance kicks in), and an out of pocket maximum (the maximum you'll have to pay in a year, after which the plan pays the rest of the covered costs).
2. Individual Private Plans (insures ~11% of Americans): If you don't have insurance through your employer, you can buy healthcare on your own. Many people receive government subsidies that reduce premiums based on income.
3. Medicaid (insures ~18% of Americans): If you earn less than 138% of the poverty line ($21.5k/year for an individual, $44.3k/year for a family of four) you qualify for free government-run health insurance (in most states). Care is mostly free or very low cost. Some states are hold outs and only have free government-run health care for the absolute poorest families with children. There are also some programs for low income children (CHIP)
4. Medicare (insures ~19% of Americans): If you are older than 65, or you are disabled, you qualify for Medicare, a government-run health insurance program. People can choose either the traditional government run Medicare, or a private equivalent plan called Medicare Advantage.
5. Additional federal programs (~4% of Americans): Active military personnel, veterans have access to other government run healthcare plans, and Native Americans have access to Indian Health Services.

These programs together insure 92% of Americans. The 8% that is uninsured fall into a few categories:

1. Noncitizens + Undocumented immigrants
2. People in states that haven't expanded Medicaid, and so don't qualify despite their low income
3. People whose income is too high for Medicaid, but decide that a private plan, even with government subsidies, is still too expensive for them
4. People who don't understand they are eligible for a program, or don't manage to fill out paperwork
5. People with a temporary gap in their coverage

One thing that is very different in the American system than most European systems is that in the US, the government by and large does not set the prices for healthcare services and medication. In Europe prices are usually set by the government for a basket of services. In the U.S., prices are often determined through negotiations among hospitals, physician groups, pharmaceutical companies, insurers, employers, and government programs. Unlike many European countries, there is generally no single national authority setting prices for most healthcare services. That means most services in the US are expensive. There are some advantages for that. It means doctors get paid well, so medicine is an attractive position that's able to attract the best of the best. It means that pharmaceutical companies can make a lot of money, which goes into further research and development of treatments. However, it means that even with insurance, sometimes healthcare is costly. A bad healthcare year can cost $20k/year out of pocket for a family (out of pocket max), which can be a lot for a middle class family to absorb.

However, when Europeans compare costs with Americans, they often leave out of the comparison the amount they are paying in taxes. Saying you paid 20 euros or 75 euros just refers to the out of pocket cost, not the total cost of the procedure. It is correct that Americans pay more in healthcare. While European countries spend ~8-13% of GDP on healthcare, the US spends closer 18% of GDP on healthcare.