Are you talking about a Password for Sync / Firefox Accounts?

I am switching from a PC to a Mac. While downloading and installing Mozilla Firefox it is asking for my username and password. I never had one before to use Firefox that I remember. Now that I have this support account I have a user name and password. Instructions said if I set up a NEW account on the Mac, that all my preferences would be reset in Firefox. :-( I am not sure that is a good thing? Gordon

You don't need a Password to use Firefox. That isn't a normal part of the installation procedure.

The username / passwords data bases across everything related to Mozilla and Firefox are separate from each other. You need to do a distinct registration for everything you want to sign up for. You can't use the same UN / PW for one service or website at another unless you purposely made them the same when you registered.

When connecting a new device to Sync you need the exact email address (the "username") and the exact Password that you last used with Sync to be able to connect to Sync and get your data back. Without that exact password you're SOL. If you forgot it or can't remember it you're SOL. https://support.mozilla.org/en-US/kb/how-do-i-set-sync-my-computer#w_connect-additional-devices-to-sync