The Peter Principle was most famously described in a book of the same name by Laurence J. Peter and Raymond Hull. The principle states that over time people in a hierarchy who are good at their job tend to get promoted until they reach a position where they are no longer competent. An example might be a great salesman who is promoted to a sales manager, despite the fact that he is a great salesman he is not well suited to managing others and so preforms poorly as a manager.
It’s an interesting idea and, despite the fact that Peter and Hull originally intended the book as satire, it has actually been the focus of several research studies and there is some evidence to support it. Interestingly a study by Alessandro Pluchino, Andrea Rapisarda, and Cesare Garofalo in 2010 found that in a computer modelled system where the Peter Principle was assumed to be true the best way to improve efficiency was to either promote people randomly, or to shortlist the best and worst performers in a group and choose randomly from that shortlist (this research incidentally won them the Ig Nodel Prize).
I don’t have much to add here other than that the principle has only been proven to work in a very limited set of circumstances and that I would hope that most companies, when promoting, would actually look at a candidates suitability for a role, not just their performance in a previous role.