Hailing from the days of ancient earth sailing vessels, a Flag Officer is usually in charge of more than one ship, and holds the rank of Rear Admiral, Vice Admiral, Admiral, or Fleet Admiral. The term refers to the tradition of hoisting a special flag, which signaled to the other ships that the ship was carrying an important person. That ship would then be refered to as a Flagship.
The term traditionally denotes any officer that commands a squadron of starships, possibly in addition to one under their direct command. Flag Officers may also be referred to as "The Brass" or simply "brass", in reference to the extra brass adorning a Flag Officer's uniform.
In modern times, a Flag Officer is typicaly in command of whole Divisions, Starbases, and entire Fleets. It is common practice for a Flag Officer to designate a starship under his command as his/her personal Flagship, using that ship as his/her Fleet's Command vessel during Fleet Operations, Diplomatic Missions, and large scale battles.
While a Flag Officer is typically considered part of the Command Division and wears the colors of such, it is not unheard of for a Flag Officer to wear the colors of the Operations or Science Divisions, if their duties lie entirely in that division.