It functions like any other kind of indemnity insurance, but in an expensive setting
Indemnity insurance is financial protection for an unforeseeable risk in the future-- like the risk that you will fall ill or be injured. This is the kind of insurance that people usually mean when they refer to health insurance. The US has other products people can buy such as discount cards, supplemental insurance, et cetera, but those are (in my experience) usually off-topic when discussing health insurance.
People benefit from this type of insurance because while it is usually impossible to determine a person's individual risk for unpredictable future events, we can estimate how often those events occur within groups (as long as those groups are large enough). So actuaries determine the rate of those events over time, such as a year, then determine what the average risk of those events are for a given group of people. Because the average risk is something that can be estimated with measurable precision, insurers can price insurance policies efficiently (can, not necessarily do). That means that individuals who buy insurance policies can live as though they are at the average risk of the group, rather than their (unknowable) individual risk.
This is how all indemnity insurance works, and it is the same in the US as it is in Japan, France, Germany, and pretty much everywhere else. It's not limited to health insurance either: auto insurance, homeowners insurance, and similar insurance products work the same way.
The major differences between the US system and others around the world are that access to health insurance in the US is uneven (not everyone has the same choices to choose from), is arbitrarily inefficient (most people access health insurance through their employers, for historical and tax efficiency reasons), has many hard-to-identify limitations (like limitations on which doctors your insurance will pay for), is hard to compare to other insurance offers (you don't get free market benefits when people can't precisely evaluate what is offered to them), is complicated and opaque (most people have no idea what the cost of their insurance is each month, or what their policy actually covers), has to deal with complicated billing practices, and most importantly that medical services in the US are expensive.
The expense is a huge problem. Not only is receiving a medical service relatively expensive by itself, but that expense tends to mean that providing insurance for that service will also be expensive.
Insurance still benefits US consumers by limiting their financial risk due to health problems. But that benefit is offset somewhat by high cost-sharing requirements (it's common in insurance policies available in the US today to have to cover the first $5,000 of many medical expenses per year, for example), and high premiums (many people struggle to afford health insurance each month, whether the reduction in risk is valuable to them or not). But the high costs of both insurance and receiving medical services cause health insurance to function mainly as catastrophic coverage. Catastrophic coverage protects against massive medical bills, but doesn't help with much else.
Health insurance in the US is provided (largely) by private companies. Those insurance companies may be owned, in whole or in part, by companies which own specific chains of hospitals and clinics, which may or may not have meaningful competitors in their area. There are public insurance plans available, but those are usually limited to specific groups (such as people older than 65, people with incomes below a certain amount). Sometimes those public insurance plans are managed by private companies. Sometimes people can get assistance paying for health insurance, and sometimes not. Insurance policies may or may not cover the same medical needs, and may or may not be subject to the same regulations.
Companies selling health insurance are regulated, mostly at the state level, which means that requirements for selling insurance can vary a lot from one state to another. Except for those insurance policies which are subject to federal regulations like the Affordable Care Act. Except when they have a waiver, meaning that they are regulated but don't have to deal with that particular regulation.
The health insurance system in the US is a complicated mess, and there is little information available to individual consumers to navigate it and even less leverage individuals have to get a good deal.
This only scratches the surface-- there are still lots of different kinds of insurance arrangements available (HSA, FSA, HMO, PPO, network tiers, and so many others), different needs people might have (and so different benefits from insurance in different situations), but the basic answer to the question is that people in the US get the same benefits as anyone from indemnity insurance: the ability to operate at the average level of group risk rather than their unknowable individual risk. But as health insurance is generally more expensive and less efficient in the US, those benefits are less valuable than many people from other countries would expect.
(I apologize if my descriptions are unclear, but my Japanese is awful. If anything needs clarification, please let me know). すみません、下手な日本語の話せる人です。