The Remember me feature is a useful way to have quick access to your site without the need to enter your username and password each time.
Ticking 'Remember Me' will keep you logged in each time you navigate to your site.
In some cases, this may be overridden to comply with security policies. This is normally in the form of a forced log out after a period of inactivity (normally 30 minutes).
Note: This feature makes use of browser cookies. If browser cookies are cleared then you will need to log into your site again.