The Galactic Republic is the name of the interplanetary State used in the fictional Star Wars universe prior to the establishment of the Galactic Empire. The form of this government, created by the Senate, was introduced in the Prequel Trilogy. By the time of the original Star Wars trilogy, it is referred to as the Old Republic. It was a democratic, though eventually ineffectual, constitutional republic tied up in layers of bureaucracy.
The Republic began as a mutual protection and economic alliance among a number of planets in the Galactic Core. Each member world chose a Senator to represent them in the Republic Senate, a central Legislative body. Senators were ambassadors of their homeworld, and member worlds were able to maintain their government and society in accordance with local beliefs, customs, and traditions. There were a wide variety of different local governments along the political spectrum: from Monarchies to Republics to Hive-like communes. In some systems, the senator was elected to that post; in others the world government appointed the senator. Naboo's monarch appointed their senator, while the Alderaan Council of Elders elected their senator out of their own ranks, usually the heir to the Royal House of Organa and their bloodline, as the heir was also the leader of the council.
When the Republic's power and influence expanded, many new areas of the galaxy were incorporated into the Republic. A reorganization of Senatorial representation occurred 1,000 BBY during the Ruusan Reformation. The most common organization for these new territories was to group regions into Sectors of about 50 inhabited worlds. Each sector is represented by a Senatorial Delegation. When the number of sectors became too large, sectors were organized into roughly a thousand regions, each represented by one delegation to the Senate.
The Senate served as the governing body of the Galactic Republic, while the Jedi Order served as its defenders. The Senate, and therefore the seat of government, was established on the planet Coruscant, with coordinates 0-0-0 in the standard galactic coordinate system, signifying its central location in the galaxy.