Thirty nine responses, and only one has come close to hitting on the most important issue.
The advantage of employer-provided health care is that it is a way to break the problem of information asymmetry.
Insurance markets in health care have a serious problem - An insurer doesn’t have good information about the state of health of people who are seeking to be insured. Therefore, the insurer has to set a price that is high enough to cover the people who are high risks. This prices out the people who are low risks, which means the aggregate population of insurees have worse health than average. This causes insurers to raise prices higher, which prices out the next-healthiest people on the margin, and so on.
This is information asymmetry, and it causes a market failure in insurance markets. Insurers try minimize this problem in several ways. One is to require health screenings and medicals for applicants. But people lie about their health, and medicals don’t reveal all. So it’s only a partial solution.
This problem exists in other insurance markets to some degree, but the severity is much greater in health insurance because the consequences of picking up a poor risk client are severe. If you get the risk wrong for an auto insurance applicant, the odds are low that you’ll get hit with millions of dollars in cost. More likely, the driver will get a few tickets or get in more than one minor accident, exposing the risk, and the insurance can dump the client after only paying out a few thousands of dollars. But if you pick up someone who is a high risk for dialysis or AIDS or some other expensive condition, it can cost hundreds of thousands or millions of dollars.
What insurers really want to do is pick up a clientele made up of a random selection of individuals across society. Then their actuaries can apply statistical methods to figure out the cost of the risk they are taking on, and price themselves accordingly. But how do you do that? Well, a good approximation is to set up health care through employers. Unless employees are working there specifically for the health coverage, this should ensure a pretty good sampling, at least within that industry.
So that’s why employers offer health care - because they can offer it much more cheaply than individuals can typically get, and therefore it gives them a way to attract employees. Note that many of these programs are not optional, or if they are, opting out doesn’t save you much. They also go out of their way to ensure that even if a spouse is insured for the family, there is some extra benefit to maintaining both insurances. This is intentional, to prevent the same kind of selection problem that exists in the individual insurance market.
So, short answer - insurance is commonly offered through employers because employers offer a way for insurance companies to find the kind of clients they need to price their product efficiently, and this has caused employer-based insurance to have a big market advantage over privately-sought insurance.
In the same vein, professional associations and unions often offer insurance programs - life insurance, car insurance, home insurance, etc. The power of selecting from a large group of random-risk individuals makes such insurance a good value and the market organizes itself accordingly.