When the Rebel Alliance re-established the Old Galactic Republic after the downfall of the Galactic Empire, it became known as the New Republic, just as the original Galactic Republic had become known as the Old Republic by that time. The New Republic was founded on the same premise on which the Old Republic had been established twenty-five thousand years previously: to have a representative parliamentary body govern the galaxy in a fair and equal manner. It was designed to eradicate the shortcomings that brought about the Old Republic's downfall. The New Republic was protected by the New Jedi Order which was established by Jedi Master Luke Skywalker, just as the Old Republic was once protected by the Old Jedi Order.
Although this description of the New Republic is considered canonical, any further details of the New Republic are explained solely in the Expanded Universe.