In the end the mandate stands because it is a tax not a penalty and the federal government can't withhold all medicaid money from states if they don't expand who they cover under medicaid. But that one problem can be severed from the rest of the act, so the rest of it stays. Ginsburg, Kagan, Sotomayor and Breyer would have found the mandate - whether penalty or tax - was fine under the commerce clause. Scalia, Alito, Thomas, and Kennedy think the whole law was bogus and would have killed it. It's a long, but ultimately not that complex, decision. The ramifications? Anyone's guess except that everyone will be in the healthcare pool now, which is a boon to insurers and, hopefully, ultimately leads to a reduction in costs. But knowing insurance companies, that's doubtful.
Below is a complete analysis of the opinion from my legal perspective.