It simply means that Firefox says your browsing can't be tracked using the browser.
History, site logins (in cookies) etc. can't be tracked.
For instance if you're cheating on your partner, (s)he will not be able to track find out using your browser history.
Theoretically the same goes on for authorities in case you use your browser for illegal activities. Though authorities have more advanced tools and more options to track you online.
Some data will most likely be recorded on your hard disk, since some data like logins is needed for using a site.
I assume it will be securely removed when exiting the browser session.
Not using your ISP's dns servers and using an encrypted connection, a vpn or a proxy helps to prevent your ISP from being able to track you.
In some cases other can though like the owner of a proxy server.
Anyone who has physical access to your computer can install all kinds of software to track your online activity's and log every keystroke you do.
In case of using someone elses computer, if you have access to USB ports on a computer you can use a Firefox version on a USB stick.
In that case the data is recorded on the stick and not on the hard disk.
Post edited July 24, 2009 by HertogJan