Article 2, Section 1 says: "The executive Power shall be vested in a President of the United States of America."
Compare with Article 1, Section 1: "All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives" and with Article 3, Section 1: "The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish."
Who holds legislative power? Congress. Who holds judicial power? The Supreme Court (and other courts that Congress establishes). Who holds executive power? The President.
I'm no advocate for the extreme unitary executive theories of folks like John Yoo, but the idea that all executive authority is vested in the president can't be written off as something that some crank came up with in just the last couple of decades.
Right, and the executive power is the power to execute the laws that Congress writes (plus foreign policy, armed forces, and a bunch of procedural stuff — Constitutionally quite weak actually [by design])
That is the power that’s vested in the executive