That is the power that’s vested in the executive
Take, for instance, the executive power "to grant Reprieves and Pardons for Offences against the United States" (Art. 2, Sec. 2). There is a pardon attorney who advises the president, but it is solely the president who has the executive power to grant the pardon; in that sense the president exercises the pardon power exclusively (or phrased differently "to the absolute exclusion of others").
Congress writes the laws, the executive (led by the President) executes them.
Not sure what your pardon example is meant to illustrate.
Of if one prefers to have it from directly from Chief Justice John Marshall, Marbury v. Madison, 5 U.S. 137 (1803):
"By the Constitution of the United States, the President is invested with certain important political powers, in the exercise of which he is to use his own discretion, and is accountable only to his country in his political character and to his own conscience. To aid him in the performance of these duties, he is authorized to appoint certain officers, who act by his authority and in conformity with his orders.
In such cases, their acts are his acts; and whatever opinion may be entertained of the manner in which executive discretion may be used, still there exists, and can exist, no power to control that discretion. The subjects are political. They respect the nation, not individual rights, and, being entrusted to the Executive, the decision of the Executive is conclusive. The application of this remark will be perceived by adverting to the act of Congress for establishing the Department of Foreign Affairs. This officer, as his duties were prescribed by that act, is to conform precisely to the will of the President. He is the mere organ by whom that will is communicated."