Wow, are you likely to get an earful over this. Here's my perspective (not a neutral one):
The "individual mandate" part of the Affordable Care Act (ACA) requires you to carry health care insurance. However, supporters claim that because the risk associated to insurers is now spread out over a much larger segment of the population (those who would normally decline health insurance are obviously less likely to need it), the cost to individuals in terms of premiums is likely to decline. In other words, they're betting that the cost of your insurance is likely to decline. Personally, I think that's likely... for insurers, anyway. Whether insurers pass these cost savings to individuals is a craps shoot. When Massachusetts (under, ahem, Governor Romney) passed a law with an individual mandate, premiums fell something like 40% at the same time that it was rising nationally.
Another big part of the bill is the "pre-existing condition" clause: basically, an insurer cannot deny you coverage because you already have a medical condition that they don't want to cover. There was some worry among ACA boosters that the court might strike down the "individual mandate" part without the "pre-existing condition" part, which would have been catastrophic to the risk pools: seven states have tried passing pre-existing condition laws without the individual mandate, and it went very badly for all of them. So if it turns out that you come down with some kind of chronic or severe condition, it can no longer be used as a reason for an insurer to deny you insurance.