The New Republic was the name of the galactic government established by the Alliance to Restore the Republic to replace the Galactic Empire following the Battle of Endor. Like its predecessor, it was often simply referred to as the Republic; less often, it was referred to as the New Galactic Republic or the Second Galactic Republic.
Formed in 4 ABY, after the dissolution of the former Alliance of Free Planets (which was formed directly after the Battle of Endor as an intermediate government), it was to become the supreme governmental authority of the galaxy. The "New" Republic was supposed to be a sort of continuation of the original Galactic Republic that had become known as the Old Republic at that time.
The New Republic was founded on the same principle that the old Galactic Republic was thousands of generations before—to have a representative parliamentary body govern the galaxy in a fair and equal manner—and it was designed to eradicate the shortcomings that brought about the Galactic Republic's downfall. The New Republic was protected in part by the New Jedi Order, which was established by Luke Skywalker, just as the Old Republic was once protected by the Old Jedi Order.
Because of the restoration of the Galactic Republic, the Imperial Remnant sometimes referred to the New Republic as the Old Order, to oppose their New Order, while in decline.