As defined by Merriam-Webster, it means this: In a hierarchy, employees tend to rise to the level of their incompetence.
Shawn Eichorst was zapped by the Peter Principle at Nebraska. He really had no business leading a Power-5 athletic department. That became increasingly evident as his six-year tenure progressed. You saw evidence, for instance, in Nebraska’s average Big Ten finish across all sports, which ranked in the bottom half of the conference during each of the past four years.
That seems perfect. A much more suitable fit. Eichorst in a secondary role makes more sense -- working behind the scenes, writing policy, being a bureaucrat.