(covers information from several alternate timelines)
On board starships, the role of the operations officer evolved from older 23rd century positions, involving some functions of the Navigator, Science officer and even Engineer (although the bulk of duties of which the Navigator and Helmsman were traditionally assigned were later integrated into the singular helmsman role). As well as manning the ops station, overseeing internal systems control, communications and sensors, operations personnel also coordinated the scheduling of resources, hardware, and system usage for an entire starship, outpost, or space station.
The operations position was typically manned by a member of the command staff of a starship, regardless of seniority. On the starship USS Enterprise-D, Chief Operations Officer Lieutenant Commander Data (doubling as Second Officer) was the most senior member of the ship's crew, after the Captain and first officer, but on the starship USS Voyager, Operations Officer Ensign Harry Kim was the most junior bridge officer.
As analytical operations relied upon knowledge of science and engineering disciplines, chief operations officers often performed the additional duties of a science officer, especially when a dedicated science officer was absent, as exemplified by both Data and Harry Kim. (TNG: "Conundrum"; VOY: "Caretaker", etc.)