When you log out, you sign off or shut down a computer system. Before you hand your laptop over so a friend can use it, you'll probably log out of your email.
When you sign in to your computer programs or applications, you log in (or log on), and when you're finished you need to log out (or log off). On shared computers — at the library, school, or work, for example — it's important to log out so your private information is protected. A log is a record, like the log computers keep of all activity, and the phrase "to log out" comes from the idea of exiting the computer's log.