Certainly it does not mean the session expires as soon as the client quits his browser. Cookie that is used to store session information on the client side, so that it can be sent to the server with subsequent requests, expires. This is the cookie that is used to track session (if necessary). So, even if you close browser window, the session object on the server still stays alive.
You are absolutely right, session is on the server and has no clue about the client's browser state.
_ __ _ __ _ __ _<br />SCJP 1.4 (95%) | SCWCD 1.4 (79%)<br />Artificial intelligence is no match for natural stupidity.