The intent of the mandate is to overcome this adverse selection problem. Adverse selection, a type of market failure, plagues insurance markets of all types, and health care is no exception. The problem is that providers of health insurance do not have as much information about the health of the people buying the insurance as they have about themselves. The health insurance companies try to overcome this informational disadvantage through check-ups prior to granting coverage, health histories, and other means, but even so individuals are better informed about their current health and their health histories than the insurance companies.
As I explained in more detail, this can cause health care markets to break down: Here's the core of the argument:
"If insurance is offered in this market at somewhere near the average cost of care for the group, people will use the superior information they have about their own health status to determine if this is a good deal for them. All of the people expecting to pay less for health care than the price the companies are asking for the insurance will drop out of the market (the young and healthy for the most part; all that is actually needed is that some people are willing to take a chance and go without insurance). With the relatively healthy people dropping out of the insurance pool, the price of insurance must go up, and when it does, more people drop out, the price goes up again, and this repeats until the market breaks down and nobody (or hardly anybody) can purchase insurance."
In order for these markets to work, health insurance must be distributed over a wide variety of people so that the average cost of care will be affordable, and to stop the markets from breaking down. One way to ensure that the pool is broad-based is to require that anyone who might need health care -- i.e. everyone -- purchase health insurance, i.e. through a mandate.
A mandate is not the only way to ensure that a broad swathe of the population purchases health insurance in a common pool. For example, subsidies can also encourage many people to enroll. If enough people enroll because of subsidies, it will function much like a mandate. But a mandate along with fines to enforce it is the most effective way to ensure that the pool is large enough, and includes enough people who do not expect significant health care expenditures, to keep the cost of insurance low.