Watch How to Sign out or Log Out of Google Apps (Gmail, Calendar, Docs, Groups, and Sites):
As an added security measure, it's a good idea to sign out of your Gmail or Google Apps account before you close your browser.
To sign out of Gmail or Google Apps, click on your email address in the top right of your screen and select Sign out.
You may not want to sign out each time when using your own PC, but it is particularly important to sign out if you are accessing your account on a shared computer or public network. However, if you forget to log out, you can log out of all previous sessions the next time you are at a computer.