Firefox stores all it knows about you in your profile. Your profile is the directory under which Firefox stores all it knows about you your preferences, your saved passwords, your cookies, your browsing history, cache, your set of installed add-ons, etc. Delete your profile, and Firefox will be forced to start its relationship with you over from scratch.
Each user on a given computer has one Firefox profile, and that's usually that. However, it's possible to set up multiple profiles for one user. Normally, that's only useful if you're doing development, e.g., debugging an add-on or something. However, since the profiles are completely separate, having multiple ones could also be useful to prevent information leakage, such as we are discussing. It has the same effect as using different browsers without requiring you to use a different browser.
You can learn how to set up multiple profiles here.
Interesting! Thanks.
Another advantage is that you can run it from a thumb drive and take your bookmarks and settings to another computer.