Let's start with used cars. "The Market for Lemons" by George Akerlof is a famous paper in economics demonstrating how markets can break down when buyers and sellers are differentially informed. For example, suppose that there are 1,001 used cars worth from $0 to $1,000, i.e. one car is worth $0, one is worth $1, the next is worth $2, and so on up to a car valued at $1,000. Assume that the car owners can assess the value of the cars they are selling accurately, but buyers can't discern any difference in quality from examining the cars. That is, sellers are better informed than buyers about the car's quality.
In such a market, a buyer would expect to receive a car of average quality, and the price would settle at $500 (the exact price doesn't matter, all that's required is that the market sets some price below $1,000). But at a price of $500, all the sellers with cars valued from $501 to $1,000 would withdraw their cars from the market since the price of $500 is less than their cars are worth.
At this point, the only cars left on the market are valued between $0 and $500, and with buyers once again expecting to receive a car of average quality, the price would fall to $250. At this price, all the people with cars valued from $251 to $500 would take their cars off the market, and the cars left on the market would now be valued between $0 and $250.
The process repeats itself, the price drops to $125, more cars drop out, and this continues until there is just one car on the market selling for $0. That is, the market for used cars breaks down.
The technical term for this is an "adverse selection" problem, and there are many ways to solve it. The buyer can hire a mechanic to determine the value of a car before the purchase; the sellers can offer insurance against the car breaking down; the sellers might have a desire to maintain a reputation for quality (dealers selling cars that fall apart shortly after purchase will lose their reputations and go out of business), and so forth.
What does this have to do with health care? The adverse selection problem is one of the reasons we need an individual mandate for health care insurance (i.e. a requirement that everyone must purchase insurance that is part of the proposed health care reform package).
To explain how the adverse selection problem arises in these markets, note that people purchasing health insurance generally have better information about their health status than the people selling the insurance. 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 the result is just like in the used car example above: The market breaks down and nobody (or hardly anybody) can purchase insurance.
But since we do not want people ruined or unable to get care when they are struck with a costly health problem, we need health insurance, and that insurance must be distributed over a wide variety of people so that the average cost of care will be affordable. 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. (For a further discussion of these issues, see here.) In the past, the broad-based pools needed to make insurance work were obtained through a large tax break to induce firms to provide insurance to their employees, combined with a requirement that if the insurance is offered, it must be available to all employees. But the steady erosion in the employer-based system is one of the motivations for reforming the health care system.
Without an individual mandate, the health insurance market is likely to break down due to the adverse selection problem, but such a mandate can place a considerable burden on some households. Thus, while the individual mandate is necessary to make these markets work, it is also necessary to provide subsides to lower and middle class households who wouldn't be able to purchase the insurance without such help.