The US pays twice as much for healthcare per person as the average western country, and supplies a lower quality of care. So where does all that extra money go to?
Some of it goes to administrative overhead (it costs a lot of money to pay the people at your insurance company who are looking for excuses to deny you coverage). But a larger fraction goes towards the profits of the insurance companies. People invest in these companies (often as part of a 401k or other retirement plan) and get back a profit (at the expense of those who pay insurance premiums and consume healthcare).
But not all of a company's profits go immediately back to its investors - any reasonable company will spend some portion of their profits on research into ways to make even more money in the future. In terms of medical insurance companies, this generally means medical research - research into new techniques, medicines and gadgets that improve the state of the art and make us all healthier in the long run.
So if the US switches to public medicine, what happens to the state of medical research? If the massive profits go away, will the research money dry up too? I have heard concerns that socialized medicine will cause medical research to grind to a halt, leaving the entire world with 2009-level medical technology for the forseeable future. I don't think it will be quite that bad - there are other sources of medical research money than US insurance companies (the US government and other governments).
I hope that in the process of transforming the country to socialized medicine, the government continues the investment in medical research and changes its focus a bit. I have the impression that the direction of medical research is set at least somewhat by the treatments that will make the most money rather than the treatments that are medically best. Drug companies pursue research on drugs that they can patent, not new uses for existing drugs on which the patents have expired. Cures are pursued at the expense of prevention and finding causes. With a change in focus we can hopefully get more effective research for less money overall.