Much as I'd hate to contradict LordShryku's statement or come off as a smart-aleck, but sessions are destroyed when the client closes its end. A session is meaningful only in the context of state maintained between server and client - if either end drops its handle on the session, the session ends.
Due to the nature of the http protocol, if either client or server drops its end of the session the other won't notice and will be left holding a lump of useless data. Usually it's the client that drops first. Then the server is left holding a session ID and corresponding session data (this is what LordShryku's referring to as "the session") sitting around with no-one to share it. But for all the server knows, the client is still out there, holding up its end, and might come back with its session ID to continue the session. (Eventually, of course, the server has to drop its end too, or it will bog down with ancient session data clogging its pores - but it has to wait at least a little while.)
Maybe I'm being pedantic, but I do think that it's best if confusion is avoided.
If the browser is closed then it should be losing the session ID. If it's not then either the session ID is hanging around somewhere to be picked up again when the browser is restarted (in a URL?) or the browser's not being closed after all.