In Plain English: The Affordable Care Act, including its individual mandate that virtually all Americans buy health insurance, is constitutional. There were not five votes to uphold it on the ground that Congress could use its power to regulate commerce between the states to require everyone to buy health insurance. However, five Justices agreed that the penalty that someone must pay if he refuses to buy insurance is a kind of tax that Congress can impose using its taxing power. That is all that matters. Because the mandate survives, the Court did not need to decide what other parts of the statute were constitutional, except for a provision that required states to comply with new eligibility requirements for Medicaid or risk losing their funding. On that question, the Court held that the provision is constitutional as long as states would only lose new funds if they didn't comply with the new requirements, rather than all of their funding.
What the principled reason behind this piece of judicial activism is is unknown. I don't think there is one. If Medicaid were repealed, and then re-passed in expanded form, there would be no limitation on the federal government's ability to condition all Medicaid funds on compliance with all provisions of the act.