They store whatever info you give them only for that browsing session: once you close the browser, your 'session' is over and all session information is gone.
On any page where you plan to use session variables, you start by calling:
session_start();
I should note that even if you just want to read (and not write) session variables on a given page, you still have to call that function.
<?php
session_start();
if (isset($_POST["name"])) {
$_SESSION["name"] = $_POST["name"];
?>
<p>
Thanks!
<a href='continue.php'>Go here for your message</a>
</p>
<?php } else if (isset($_SESSION["name"])) {
echo "Hi {$_SESSION["name"]}!";
echo "<a href='logout.php'> Logout </a>";
} else { ?>
<form action="continue.php" method="POST">
<p>
Name:
<input type="text" name="name" />
</p>
<input type="submit" value="submit"/>
</form>
<?php } ?>