Shared risk/cost. Right now the people that don't really need health insurance don't get it, and the peopel that do need it get it, but end up costing insurance companies more than they pay in premiums.
So like, if I'm a baby boomer there's a pretty good chance I will need a major operation (like say knee surgery) in 10 years, and I will probably need a handful of regular medicines for blood pressure etc. And I'm more likely to go to get a CT scan of my chest or something. The cost of those items may well end up exceeding the amount I pay for my premium.
Now, if I'm a young healthy guy, I may pay 200$/mo but I almost never go to the doctor. The money I am putting into health insurance is more than I am recieving in services.
The problem right now is that the people from the second group don't really use insurance, or at least not nearly as much as the people from the first group. The people in the second group who have insurance (like myself) have to pay higher premiums to make up for all the other people in the second group who don't have insurance. So when the number of people in the second group increases the burden I have to pay to support those in the first group decreases.
Edit: Another point is that there are a lot of people without health insurance who don't catch health issues early and end up going to the ER or getting treatments that are wayyyyy more expensive than it would have cost early on. Since they are unable to pay their bills the expense of their visit ends up getting put on the second group.
Now, by forcing them to buy insurance (or fining them), means that they may well get the preventative medicne they need to ensure that the cost of their ailment is mitigated and controlled early on.
So, another cost saver.