A Military governor was the title used for a military officer whom was given governmental control over conquered territory.
Kor was made military governor of Organia, when the Klingon Empire occupied the planet in 2267. As military governor, Kor appointed a liaison between his forces and the Organian population and issued the rules and regulations of the Empire. Nevertheless, he considered the posting as a military governor as not much appalling, even less so because the Organians put up no resistance at all. (TOS: "Errand of Mercy")
Presumably, being removed from active battle and placed in a bureaucratic function is not considered very honorable by the Klingons. Although not explicitly stated, it is possible that Klingon Governors Torak and Vagh were also military governors, as they wore uniforms of the Klingon Defense Force.