The purspose of the turnchat is to actually play the game! The DP plays the game using the instructions posted by the officials in the Turn Chat Instruction Thread, and reports in the chat what they are doing and what is happening in the game. Everyone there joins in offering advice and cheering our troops on. As for how long they go on for - 10 turns a time normally, in some circumstances it could be up to 13, if something occurs that needs to be discussed less. In terms of time that could be a couple of hours early in the game, recently we had one last over 17 hours! - but that could be partly because I'm rather slow as DP! Don't worry if you're not there at the start, or can't stay to the end; pop in when you can and see what's happening (looks like the Aztecs get it next).
Look in the Game Saves and Chat Logs Thread stickied in the main demogame forum for links to recent game summaries, - the most recent are at the bottom.