The Peter principle is an observation about a commonly-seen pattern in hierarchical corporate cultures in which employees are promoted based on current performance rather than aptitude for the roles they are being considered for.
According to the Peter principle, employees continue to be promoted as long as they perform well in their roles; as a result, they rise to their level of incompetence: the point at which they fail to do a good job. That pattern negatively impacts employee productivity and corporate performance because it tends to mean that people end up in positions where they are incapable of doing a good job and that, furthermore, they tend to stay in those positions because -- since they aren't performing well -- they are not promoted. Eventually, as the Peter principle plays out, all positions in an organization could be held by individuals who are incapable of fulfilling their roles.
Laurence J. Peter first formulated and named the phenomenon in 1969, in a satirical book "The Peter Principle," where he stated that "In a hierarchy every employee tends to rise to his level of incompetence ... in time every post tends to be occupied by an employee who is incompetent to carry out its duties ... Work is accomplished by those employees who have not yet reached their level of incompetence."
Peter called the tendency to "kick employees upstairs" (promote them to management positions) percussive sublimation and suggested it was a method used to keep them from hampering more productive workers. Percussive sublimation, in turn, is related to the Dilbert principle, which maintains that the real purpose of the hierarchy is to provide managerial roles that will minimize the ability of those employees to interfere with the actual work being accomplished by more productive staff members.