The Peter Principle, named after economist Dr. Laurence J. Peter, states that "In a hierarchy every employee tends to rise to his level of incompetence." This is often seen in the 21st century in the business world and in many other kinds of organizations.
In Macbeth, Shakespeare is showing how one man of determination and ambition rises to a position in a hierarchy where he doesn't belong because he is incompetent to function effectively. Macbeth, a very brave and competent soldier, is Thane of Glamis. King Duncan rewards him for his service in battle by promoting him to Thane of Cawdor. Macbeth then takes it upon himself to try to rise to the position of King of Scotland.
He displays his incompetence on the night he murders King Duncan. He forgets to leave the murder weapons in Duncan's chamber and his wife has to take them back and also smear blood on the faces of the unconscious grooms. Macbeth should have murdered Malcolm and Donalbain that same night, but he loses his nerve and begins having hallucinations. Somehow he manages to be crowned king, but he does not know how to govern. He creates a deplorable spectacle at the banquet scene in Act 3, Scene 4, when he thinks he sees Banquo, the man he had murdered, occupying his seat at the table. He does not trust his own judgment but relies on his wife and on the three Weird Sisters. Scotland becomes chaotic. In Act 4, Scene 3, Ross tells Macduff:
Alas, poor country,
Almost afraid to know itself.
Macbeth, true to his nature as a warrior, governs by force and terror. The more despotic and tyrannical he becomes, the more desertion and resistance he brings upon himself. In Act 5, Scene 2, Angus says of him:
Now does he feel his title
Hang loose about him, like a giant's robe
Upon a dwarfish thief.
At the end of the play Macbeth is doing the only thing he knows how to do competently: he puts on his armor and goes out to fight an overwhelming army. He is a good example of the Peter Principle at work in ancient Scotland.