Explainer, Please

The Congressional Budget Office says that if it passes health care reform will save $81 billion over 10 years. Can someone write an easy to understand blog post explaining to an ignorant non-wonk like me how you cover millions more people, avoid government rationing, and save all that money? I’m asking in earnest. I haven’t followed this bill very closely, and this result seems utterly counter-intuitive to me. What is it that I’m missing?