Starfleet is an organization based in San Fransisco on Earth and a founding component of the United Federation of Planets. Starfleet is a major part of Earth's military by 2151 (Star Trek: Enterprise) and continues through the 24th Century (Star Trek: TNG Era) Starfleet's primary objectives are to insure tactical saftey of Earth its colonies, and all citizens of the UFP. Starfleet is also a diplomatic and scientific organization. Starfleet, operate hundreds of starships, starbases, outposts, colonies, warships and other installations.
Starfleet is similar to the Navys of Earth in the 20th century with Admirals, Captains, Commanders, Lieutenant Commanders, Lieutenants, Ensigns, Chief Petty Officers, Crewman and other ranks. The commanding officer of a Federation Starfleet Starship is usually a Captain in rank.
Admiral Poole was Commander of Starfleet Operations in a major sector of the Federation in the 2280's. Poole was the flag officer that issued Captain Paul Edwards' orders on a regular basis. Admiral Shore is the Admiral in charge of sector in the 2350's when the USS Montana made its historic venture into the 24th century.