You can look at the 113 page opinion (pdf), or just accept the New York Times’ summary:

The court turned aside a broad challenge to one part of the law, which established the Public Company Accounting Oversight Board to regulate the accounting industry. Some commentators had forecast that the court might throw out the entire law because of problems with the way the accounting board is appointed, but the justices refused to do so.

Instead, in a 5-to-4 split, the court found that the way members of the oversight board could be removed was unconstitutional.

As a result of that decision, the Securities and Exchange Commission, which appoints the five members of the board, will now be able to remove members at will, rather than only if there is good cause.

“The Sarbanes-Oxley Act remains ‘fully operative as a law’ with these tenure restrictions excised,” wrote Chief Justice John Roberts in the majority opinion.

The court majority concluded that the Constitution did not allow two levels of “good cause” review to separate the president from firing people in his administration. He needs good cause to fire S.E.C. commissioners, so they could not need good cause to fire people they appoint.