There are a ton of reasons why, but here are a couple of the big ones.
The US is still at the forefront of medical research and technology development in the world. However, many other countries won't pay "market" rates for newer technology developed here at home, so companies often overcharge domestically as a way to recoup revenue they can't collect in other places. Note that American hospitals (particularly newer ones) tend to be obsessed with having state-of-the-art technology, and they're damn sure gonna get paid for that.
Another major factor driving healthcare costs is the increasing barriers to access for millions of people. Lots of folks don't realize this, but the US already has a quasi-socialized healthcare system mandated through Federal law. Basically, it's illegal for hospitals to turn ER patients away that cannot prove ability to pay, so folks without insurance often come to the ER for routine medical treatment because its the only way they can be seen, and they know the hospital isn't going to chase them down for their bill because they can't pay for it anyway. Who winds up eating those extra costs? Folks with insurance. I used to work in an ER and I saw this happen all the time.