In the political theory of the United States of America, The Unitary Executive is the principle that the executive branch encompasses one will, embodied in the office of the President. This principle springs from a statement in the Constitution of the United States of America that
"The executive Power shall be vested in a President of the United States of America."
As with so much else in the United States government, this seemingly simple principle has all sorts of thorny connotations
All senior executive officials (those involved in policy or political decision making) in The United States are appointed by the President with the "advice and consent" of the senate. However, after they are appointed, they serve at the pleasure of the President. The President can dismiss the different cabinet secretaries (and undersecretaries) for incompetence, perception of incompetence, having differing political views, because he wants someone else in their job, to help redefine his agenda, or for absolutely no reason at all. The different executive departments of the United States are all subsidiary to the office of the Presidency, and so the President has absolute say in how they are run, and by whom.
But much as with many legal rules that regulate the common job holder or apartment renter, there is a big restriction on how the President can direct his cabinet members. While the President is free to dismiss government officials for absolutely no reason, or very trivial reasons, he can (probably) not dismiss them for faithfully doing their jobs. The President can dismiss the Secretary of Agriculture for wearing a bad tie to a cabinet meaning, but he can't dismiss him because he thinks the Secretary of Agriculture should stop inspecting food.
And the way this becomes thorny is because the President (and the executive branch) have a gigantic, multivalent mandate to administer a massive government that has to oversee many different programs, as well as to execute all the country's laws and regulations. This is why we have an executive branch: to decide how to prioritize this task. While the President's duties involve making sure that the "Laws are faithfully executed", he has to decide to do that with the finite resources at his disposal. I will use a more realistic example than the Secretary of Agriculture wanting to inspect food to demonstrate how this could be a problem.
During his campaign, Barack Obama promised that he would end federal interference in the use of medical marijuana in states where it was legal. Right after his inauguration, Obama and his attorney general, Eric Holder, made this official policy. From a perspective of politics and policy, this makes a lot of sense: the federal interference in state's decisions to legalize marijuana for medical purposes had caused political friction in these states, and from a policy standpoint, spending resources to combat a victimless crime such as marijuana use by the ill seemed like a waste of resources. Obama and Holder's actions therefore seem to be within the scope of the executive: deciding how to best use scarce resources. However, let us imagine that Holder, (or some other undersecretary within the Justice Department) disagrees with Obama's policy, and attempts to continue to investigate and prosecute the use of marijuana, which is (after all) still illegal under federal law. Can the President dismiss an official for having different priorities, if that official is still legally discharging his duties? That is the question that I don't believe there is an official answer to, and to which no answer is perhaps totally possible.
The previous example might not be a good example, if the reader's believes (like me), that federal persecution of medical marijuana is ridiculous. However, we could find many other examples that might put the issue into a different light. Suppose a President who wanted to undertake an ambitious course of highway construction ordered his EPA chief to not inspect or enforce regulations about the environmental damage that this could cause: would this be a legitimate use of the Unitary Executive. The United States has many laws and programs, and many agencies to enforce them, many of which will at times be at cross purposes. When does the President's attempts to put together a coherent executive program make the step into undermining the mandate of an individual agency?
The problem is, that even the strongest believer in a Unitary Executive has to admit that the executive is only one branch of government. When the Unitary Executive makes the step into totally ignoring laws, or enforcing laws to a point outside their original scope, than the Unitary Executive becomes a Unitary Executive & Legislature, something that is obviously totally contrary to the point of the office. The question then becomes when is the Office of the Presidency making a legitimate attempt to prioritize aims, and when are they undermining the congressional mandate of an executive department or official.