they are not connected to the Internet.It uses Google Gears technology to store the emails in the user's machine.Its a competitor
to the products like Microsoft Outlook which are used for accessing email in absence of Internet.
But there is twist in the story. When you enable off line mode in GMail it stores emails in your systems and also installs a desktop
shortcut. So if you are in off line and if you click on that shortcut you will be shown page as below
It means if your laptop or netbook stolen , thief can access all your off-line messages by just entering your username. Its a serious threat since GMail off line feature holds key in its fore coming Chrome OS.It lacks the password locking facility provided by the products like Outlook.
So think before you enable off-line feature in your account .