A good place to start is HealthCare.gov. This is the health insurance exchange created by the The Patient Protection and Affordable Care Act, and is a one-stop shop for private individual market health insurance plans (note that the exchange itself is run by the government, but the health plans for sale in the exchange are all private, from the health insurance companies with which you're already familiar). People in 39 states use HealthCare.gov to enroll in individual market plans. The other 11 states and the District of Columbia have state-run exchanges, and you'll be directed to their sites from HealthCare.gov when you select your state.
Baylor Hospital, in Dallas, Texas, introduced the first pre-paid hospital insurance in 1929, offering to provide medical services to a group of Texas teachers for a premium of 50 cents a month. The plan worked on the principle of paying for the costs of care for a small group of sick individuals by spreading them out over a much larger pool. The concept caught on, and by the late 1930s, nearly 3 million Americans were enrolled in “Blue Cross” hospital plans.
There are other plans available year-round that are not individual major medical coverage. Most of these plans are not recommended as stand-alone coverage (with the exception of short-term plans, which can be adequate stand-alone coverage if you're healthy and you know that you need the coverage for only a short time; they are usually not at all adequate for longer-term coverage). These plans are not regulated by the Affordable Care Act, which means they can exclude pre-existing conditions, impose dollar caps on your coverage, and don't have to cover the ACA's essential health benefits. In most cases, these plans cannot really be compared with an employer-sponsored plan, since the coverage will be so much lower quality. If an insurance offer sounds too good to be true, read the fine print carefully. It may end up being a poor substitute for real health insurance, and you don't want to learn those details after you have a major claim.
Public health insurance is provided or subsidized in some way by the federal government. Medicare, Veteran benefits, and insurance provided to federal employees are all examples of public health insurance. Private health insurance, on the other hand, is provided by private companies. The CDC estimated that in 2017, 65 percent of Americans under age 65 were covered by private insurance.
For those who don’t have access to employer-sponsored plans, coverage on the individual market is an option. This market has changed dramatically as a result of the Affordable Care Act. Prior to 2014, in most states, individual coverage was medically underwritten, which meant that coverage was only available for purchase if the applicant was at least fairly healthy, as the insurance companies would closely scrutinize your complete medical history when you applied. Coverage in the individual market was typically not as robust as employer-sponsored health insurance; maternity care, prescription drugs, and mental health care were often missing from the coverage. And people who purchased individual market coverage prior to 2014 had to pay the whole premium themselves.