Here is Chieftess' description from an announcement up in Civ3:
The Demogame is like a huge succession game where many users (called citizens) discuss and vote on what to do next. Each term, one player (the 'designated player', or president) is elected to actually play the game. The Demogame also allows you to be any six of the advisors. The posistions don't stop there. There's the judiciary (Judge Advocate, Public Defender and the Chief Justice), along with governors for each province, or region of cities. There are currently 24 provinces in this demogame. You can sign up
here, in the Citizen Registry.
The current demogame is being played with Vanilla Civ3 v1.29f. Even if you're not the best player, or just want to refine your skills in one area, the demogame is a great place to see strategies and ask questions about why we're doing things a certain way in the game. There is also a huge storyline in the Demogame RPG, which is loosely based off of the demogame.
Even if you don't have a posistion, you can help out in other ways. Examples are helping department leaders with different department related tasks (i.e., seeing how many of each city improvements the nation has), or join one of the 'sponsered offices', such as the Cartographic Office, or the History Office.
The Demogame also has turnchats, which are listed in the
main Demogame forum. The president creates a thread for the demogame each turn, such as "Turn Chat - 1495 A.D. - Wednesday, March 26 (1:00 PM EST, 6:00 PM GMT)". In this thread, you will find the game saves, instructions for the designated player, and at the end of the turn chat, the chat log and end save of what went on during those turns. On the front page, you will also find many threads on what the demogame is.
-- Chieftess