This icon tells you that an updated version of Firefox is available. There have been several security updates since Firefox 1.0 was released last October, with the current version being 1.0.4. I’ve seen a lot of these on computers I don’t manage myself. Either it’s too subtle or people have interpreted “more secure” as “completely secure” and don’t know they need to keep up to date.
You don’t need to uninstall Firefox in order to upgrade, and you don’t need to create a new profile. These used to be true when it was still in beta, but haven’t been necessary since it hit 1.0. (There also used to be a bug where Firefox would be listed twice in Add/Remove Programs, but it wouldn’t cause any problems.)
Just clicking on the red circle will give you a chance to grab the installer. Yes, with FF 1.0 it does still need to download the whole installer—all 4 MB of it, which is still smaller that some of the updates I’ve had to grab for IE—but Mozilla is working on major improvements to the updater for 1.1.
Incidentally, if you see a blue circle instead of a red one, that means some of your extensions have updates available. Just click and follow directions.