If you are interested in more detail, here's a pretty good
rundown of the law. According to it, Romney not only signed it into law but proposed it in the first place. I haven't been paying enough attention yet to know what he's been saying about universal programs in his president-seeking activities.
But essentially it says, we've subsidized health insurance enough through various programs that "affordability" isn't an excuse for anybody not to have coverage (price goes down to fully subsidized for certain people) so it is their responsibility to go get it at certain minimal levels.
One thing I don't like about it is that catastrophic coverage would not be sufficient. That's the kind of coverage I prefer since it makes economic sense for a pretty healthy, well off, family of two. I go years without seeing a doctor and when I do I can afford to pay hundreds of dollars out of pocket if necessary and in a mini emergency many thousands would not be too strenuous on us. But if one of us gets cancer or hit by a car I would want coverage for medical expenses over, say, $40,000 or something. That I want insurance for, but I don't want insurance to pay for the $150 office visit if I get the flu or want a weird rash looked at.
So I find it a bit of a stretch to say to Bill Gates, "look you have to have insurance because if you don't and you get sick you'll be a financial burden on society."