If you want to finish your BrainKing session and make sure nobody else can access your account after you leave the computer, click on the Logout link in the Menu section. You should be returned to the main entry point of the site and after that you are successfully logged out.
Since BrainKing never stores any permanent login information on your computer, you can also finish the session by closing the web browser. However, it is always safer to log out manually, using the Logout link.