The Earthen Union is the alliance of the six nations of Earth after the ending of World War IV, with the signing of the Treaty of Bremen. It is similar to the United Nations, except all member nations have equal standing and every political entity on the planet is a member.
The formation of the Earthen Union marked the beginning of the Third Era. Therefore, at the start of The Lunar Chronicles, the Earthen Union was 126 years old, as evidenced by the fact that the years was 126 T.E.
The members of the Earthen Union all use the same currency, univs.
The formation of the Earthen Union is celebrated throughout the world as a reaffirmation of world peace. It seems that different nations celebrate it at different times; the peace festival in the Eastern Commonwealth is held in late August, while the peace celebrations in the American Republic are held in mid-July.
Throughout the series, the member nations try to get Luna to sign the Treaty of Bremen and join the Union. Presumably, signing the treaty involves some level of military disarmament, probably overseen by the other member nations.