When you check this box (Remember Me) 3rdKey.com associates your user name with the device you are using for the next 30 days, using a cookie.

Also, and this is important, I will keep the session open longer, so if someone else has access to this machine they might be able to see your passwords.

So if this is a public device, do NOT check this box. But if this is your personal device, you might want to check it so you do not have to enter your user name every time you come here. You will still need to enter your encryption keys though.