This is an axiom of organizations that says a person will be promoted to the point where they become incompetent. Over time, this means that many people will be incompetent at their jobs.
If Bob occupies Position A and is competent at it, he will be promoted to Position B which has more responsibility. If he is also competent at Position B, he will be promoted to Position C, with more responsibility.
However, if Position C proves too much for him, and he is incompetent at Position C, then he will remain there. He has been promoted to a position at which he is no longer competent, and is now stuck, which is suboptimal for both him at the organization.
Ideally, Bob would be demoted back to Position B, where he was last competent, but since individuals and organizations resist demotions in general, he is more likely to remain – permanently and incompetently – in Position C.
The term was coined by researcher Laurence Peter. It was supposed to be satire, but resonated with audiences over time. It was immortalized in a 1969 book of the same name.
Why I Looked It Up
In REAMDE, a character says to another:
Seamus, you are a living example of the Peter Principle.