Medical Insurance is one of the most controversial products from a political and economic sense in America today. Prior to 1920 there was no such thing as the amount people spent getting care was quite low. Typically up until that point a doctor would come to you and administer whatever assistance he could for a small payment.
Thus from a market share perspective it just did not exist. Only when health costs began to rise dramatically was an economic need created that was large enough to spark the offering of private health insurance. Basically the financial risk of how much a serious health crisis could pose to someone became so great; you literally had to get coverage.
Today there are many different products available to the general public. The most common type is group health insurance. Typically people associate this with a policy they get from work. This simply means that the defined group that is getting the coverage are the people at that company. Individual policies are available but they are more expensive as there is no larger group available to spread the risk of a catastrophic event.