Reference - Guides Directory (United Kingdom)

If checked, the Remember me on this computer box on member login page will remember your login email id and password unless you log out of your account. Checking this box is only a good idea if you're the only person using the computer.

If you've selected this option, then your LinksAmazon.com member account may be open to anyone who uses the same computer after you. You should never check this box if you're using a publicly accessible computer, or if you're sharing the computer with others.