I'm guessing that you've joined the busy community of Slashdot, actually. Sign up and you'll find that the login screen looks like this:
By contrast, an account on Netscape.com is far more typical:
Here's the dirty truth: most sites, when you log in, send you a 'cookie', a tiny data packet that's then handed back to the server each and every time you send a page or image request. (I think of it as a little bug that's along for the ride, though bugs and cookies typically don't mix too well). On a site that's well behaved, it marks that cookie data as temporary, to be automatically deleted when you quit the Web browser.
Some sites, however, give you a permanent cookie without telling you, and that's not good because your cookie file is often quite insecure, meaning that if anyone can touch your computer, they can probably extract your account and password pair for those sites. Not good!
The better sites offer you the option of having your login information stored with a cookie between browser sessions -- the remember me option -- so that if you are on a secure computer, you don't have to fuss with logging in every single morning. This is a good idea for your home computer, for example, but not a computer that's in a public computer lab or an Internet cafe.
And that's what Slashdot is referencing in its checkbox. It's the opposite of "Remember Me", really; if you check the "Remember Me" option in Netscape, it will give you that permanent cookie and you'll be logged in forevermore. If you don't check "Remember Me" you'll have a temporary cookie and next time you start your browser you'll be logging in again. Slashdot is 180-degrees from that: if you don't check "Public Terminal", then it will give you a permanent login cookie, but if you do check "Public Terminal" then it'll make sure that when you are done with that browser session the cookie-based login information will be zapped too.
You're not the only one who finds this confusing, by the way. I find it baffling why sites can't just agree on a single common approach to these login cookies...
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Pretty interesting - I was wondering the same thing, but it makes perfect sense now.
Public Terminal just means.. that you're sitting on a Public Terminal and don't want anything stored. Meh, I've missed the word terminal enough to admit I now prefer it to "Remember my password" or something like that.