Since the text of the Obamacare decision is 193 pages, here is a 100 explanation of what the Supreme Court decided:
In order for Congress to pass a law, it must rely on a specific clause of the Constitution. That way, states have areas in which they have the exclusive ability to legislate.
The Obama Administration first argued that Obamacare was valid as a regulation of commerce. The Supreme Court rejected that argument because Obamacare regulates inactivity (not having insurance).
The administration also argued that the law does not make failing to purchase health insurance a crime. Instead, the law requires those who do not buy insurance to pay a tax. The Supreme Court accepted that argument. So, Obamacare is constitutional.