The board monitors the accounting industry, especially the four largest accounting firms that handle the books for many of the most prominent corporations. The Securities and Exchange Commission chooses the board's members, with consultation by the Fed and the Treasury Department.
The DC Circuit upheld the board's selection process, saying that past Supreme Court precedent concerning adminsitrative agencies supported SOX's constitutionality.
Ever since its passage in 2002, SOX has come under fire by the business world for imposing cumbersome requirements for accounting and reporting.
Court to rule on Sarbanes - Oxley (SCOTUSblog)
Breaking: Sarbanes-Oxley to the Supremes (The Volokh Conspiracy)