If you check the 'Remember Me' box, this site will set a 'cookie' on your web browser which will 'remember' your email address. This means that you will not need to re-type it each time you visit the site.
Checking the 'Remember Me' box is a convenient, time-saving option if you're logging into this site from your own computer. If you share a computer, however, you may not want to select the 'Remember Me' option.