Oh!! OK!!!! Thanks Liscab and Classwife.
I guess I'm showing my ignorance here. In some sites, if I check remember me, it recognizes my IP as soon as I enter the site. I don't really want that, due to horror stories I've read about security.
A friend had her pc taken over by a hacker - she couldn't even use her keyboard and he was using her computer, IP, etc. for his/her hacking.
Maybe I'm not as educated as most when it comes to the internet, but I try to avoid any problems.
I'll check "remember me' from now on, as long as the "remember me" status stops when I log out.