If you check the "Remember Me" checkbox, MyADC will place a cookie on your system that remembers the username you are using to log in. The next time you visit, your username will be filled in for you. Your password is not stored in the cookie.
A cookie is a small file stored on your computer. Your browser may ask you for permission before storing the file. If your browser is set to reject cookies, your username will not appear on your next visit.
If you are accessing MyADC on a public computer, you should not check the box. If you do, others will see your username when they visit.