An adjutant was a staff officer who assisted a commanding officer in issuing orders. An adjutant functioned as an executive officer of sorts.
Admiral Leyton and his adjutant, Commander Benteen
Commander Benteen functioned as an adjutant to Admiral Leyton before being promoted to captain of the USS Lakota. (DS9: "Homefront")
Sarish Rez was Shakaar Edon's adjutant in 2372. (DS9: "Crossfire")
In 2374, Captain Benjamin Sisko was made Admiral William Ross' adjutant during the Dominion War. He replaced Captain Bennet in the role when she was put in charge of Seventh Tactical Wing. (DS9: "Behind the Lines")