The seal adopted by the New Republic Provisional Council as the Insignia of the New Republic was based upon the symbol of the Alliance that preceded it, the blue crest of the Alliance -which was in fact featured in red more often. It was set within a circle of stars that represented the galactic community. The circle is trimmed in gold, symbolizing the right of the people to govern themselves.
Behind the scenes
Older sources mentioned it was taken from the seal of the Old Republic itself, but as none of the different seals of the Old Republic looked like the Rebellion's crest, this information seems now deemed non-canon.