Author F. Heylighen sums it up pretty well:
The principle is based on the observation that in such an organization new employees typically start in the lower ranks, but when they prove to be competent in the task to which they are assigned, they get promoted to a higher rank. This process of climbing up the hierarchical ladder can go on indefinitely, until the employee reaches a position where he or she is no longer competent. At that moment the process typically stops, since the established rules of bureacracies make that it is very difficult to "demote" someone to a lower rank, even if that person would be much better fitted and more happy in that lower position. The net result is that most of the higher levels of a bureaucracy will be filled by incompetent people, who got there because they were quite good at doing a different (and usually, but not always, easier) task than the one they are expected to do.If you think about it, Sarah Palin is a prime example of The Peter Principle, proving that she met her level of incompetence when she became governor of Alaska, only to face numerous charges of ethics violations. Palin's solution was to step down from the position she could not competently maintain, opting for a job that essentially has a higher ceiling for incompetence - celebrity entertainer.
Without having to act in an official capacity, Palin is free to make all the gaffes she can, like claiming her stint as Alaska's half-term governor qualifies her to become president of the United States, despite her numerous failures. Let us just hope that Palin never finds herself in a position that excedes her comfort zone again.
Come to think of it, Sarah Palin seems to exemplify The Dilbert Principle more so then The Peter Principle. The Dilbert Principle comes from the Scott Adams comic strip Dilbert, of course, explaining that a "person who has never been competent at anything at any point in time can still be promoted into management."