The United States Constitution provides that the president "shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the Supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for." (Article II, section 2).
The president nominates all federal judges in the judicial branch and specified officers in cabinet-level departments, independent agencies, the military services, the Foreign Service, and uniformed civilian services, as well as U.S. attorneys and U.S. marshals. The vast majority are routinely confirmed, while a small but sometimes highly visible number of nominees fail to receive action or are rejected by the Senate.
In its history, the Senate has confirmed 126 Supreme Court nominations and well over 500 Cabinet nominations.