If you check the "Remember me" box, you will be remembered by the site even when you close your browser or switch off your computer. As long as you do not explicitly log out, you will not need to log in next time you visit the site.
If you wish to, you can force the site to forget your identity by using the logout button. If you do this, next time you visit the site you will need to log in again.
For security reasons, we recommend that you do not use the "Remember me" option if you are using a shared computer.