The Pardon Clause in the U.S. Constitution gives the President very broad authority when it comes to executive clemency, but that power is not absolute. For example, the Constitution does not permit the President to pardon violations of state law, and most felonies are prosecuted at the state level. In addition, the President cannot issue a pardon in a civil matter or impair the vested rights of third-parties.

 
For more details about the laws that define executive clemency, read Samuel Morison’s essay, “The Constitutional Law of Pardons.”