The judicial powers of the president of the United States are the power to pardon and grant reprieves, the power to appoint federal judges and the power to appoint justices to the Supreme Court. The power to appoint judges and justices is limited in that those appointments must be approved by Congress. Conversely, the power to pardon and grant reprieves is quite broad.
The power to pardon stipulates that the offense must be against the United States. The president is allowed to pardon an individual for an offense at any time following the commission of the crime, regardless of whether the person served his sentence. A pardon wipes the person's slate clean of any effects of the conviction. A presidential reprieve, on the other hand, does not take away the individual's guilt, but simply lessens his punishment.
There are more than 800 federal judge positions throughout the country, but all who receive appointments are appointed for life. Presidents often rely on recommendations from other individuals and agencies to help with the nominating process. Members of Congress, the Department of Justice, the FBI and the American Bar Association are often good resources. Supreme Court justices are also appointed for life. Not all presidents have the opportunity to nominate a Supreme Court justice, but those who do have an impact on American law for years after they leave office.