Configuring my web app to be used simultaneously
You should separate your games. I would do this by making a Game model that has its own board. If you are planning to make this a multi-player app, I would also give the model player1 and player2 attributes so that you can determine which board to show to a particular user.
I don't have a great way to keep the games in sync across multiple tabs other than to have some javascript that refreshes the board at a certain interval.
I am building a tic-tac-toe game using django. Different users will be simuntaneously playing the game at different places. So, how does the server store the states of game board for different persons?