An example of the Peter Principle at work: imagine a high-performing sales person who gets a series of promotions. The first promotion could be to a sales manager - perhaps that could go well - because he could mentor others on successful strategies and tactics of turning prospects into clients. Noting the success of the team, the executives then promote this manager again to run a business
This manager is now running a team of salespeople, programmers, engineers and marketers. Now, the successful sales manager could stumble. He could achieve at managing some of the employees since he is familiar with their roles and the problems they encounter. However, he might not understand the technology… or the management style that motivated the sales reps might only alienate or irritate the more reserved programmers.
The manager, accustomed to being a star, starts to get average performance numbers and resistance from his staff. After a while, his heart isn't even in it anymore, so he never gets a promotion again. Because rules in administrative bureaucracies make it difficult to demote someone, he then stays in the position until he retires (or until the company goes under due to mismanagement!)
Talented people working under this manager get very frustrated because he is not perceptive about what makes one employee more effective than another or he implements ridiculous policies so the competent people either become apathetic or leave.
The employee's incompetence after promotion is not because he lacks skill; it is simply because the skills it took him to get the job did not prepare him for the job he won. They are two different sets of skills. Employees do not want to be incompetent, but management puts them into positions where that is what they will become.
The concept is often ignored by management and management consultants because to admit it is to admit their own level of incompetence. Also, the people who are making the wrong promotion decisions are results of the Peter Principle. This combined with the frustrated, competent employees leaving, the organization begins to spiral downwards.
A way to avoid this problem is to only promote people when they have already shown the skills necessary to succeed at the next position. Another solution is to think of other ways of rewarding success such as creating a "specialist" position instead of assuming everyone will be competent at (or wants to be) in leadership.