We usually ask and answer questions directly on here... just for future reference.

The session_start is used at the top of files to create a user session. This is one way and the most common way of keeping track of a user being logged in. When you create a login script, after verifying the user and their account, you would set a session variable like
$_SESSION['authorized'] = true;. The on each page, to keep them in the session, you would use the session_start() you see as well as checking the session variable to see if it exists. If it exists it means they went through the login screen and got validated. Here is the general idea...
CODE
<?php
// Needed to start the session on every page.
session_start();
// If the session variable is not set or does not equal true, send them back to the login page.
if (!isset($_SESSION['authorized']) || (!$_SESSION['authorized'])) {
header("location: login.php");
}
?>
Usually what happens is that if you want them to be able to logout, you destroy the session using
session_destroy(). Look at the php.net website under sessions for more information on how sessions work and how you cause use them to keep a user session going and valid.
As for the money portion of the game, where you store that field is up to how you want to design the game. I have designed games where the money was part of the user's table, and there have been games where I put it in a "resources table" along with things like wood, stone, gems etc. That resources table would then have a key field that links back to the user's table.
Hope this answered your question.

"At DIC we be session hugging code ninjas!"