A governor is a political leader. Several colony worlds are run by governors.
Donald Cory was governor of the penal colony on Elba II in 2268. (TOS: "Whom Gods Destroy")
Robert Wesley was governor of Mantilles in 2270. (TAS: "One of Our Planets is Missing")
Karnas was the governor of Mordan IV in 2364. (TNG: "Too Short a Season")
Vagh was the Klingon governor of Krios in 2368. (TNG: "The Mind's Eye")
Torak was the Klingon governor in charge of Sector 2520 in 2369. (TNG: "Aquiel")
Maturin was the governor of the Caldos colony in 2370. (TNG: "Sub Rosa")
Avesta was the governor of the Bajoran colony Prophet's Landing in 2371. (DS9: "Heart of Stone")
In an alternate timeline, Worf was governor of H'atoria in 2395. (TNG: "All Good Things...")