The stock Firefox browser, with that I mean the releases that are available for download on the Mozilla website directly, can be run on 32-bit and 64-bit Windows operating systems. While that is the case, it is a 32-bit application that Mozilla offers on its website.
There are 64-bit versions of Firefox, and they are made available by Mozilla for Linux distributions and Mac OS X. If you are looking for a Windows 64-bit version on the other hand, you won't find it advertised on the official project website, and will have a hard time finding references made to it on the site as well.
That does not mean that it does not exist. Mozilla was about to shut down the building of 64-bit Firefox builds for Windows, but user outcry over this made Mozilla revert the decision.
Before we look at that, it is necessary to find out about the differences between 32-bit and 64-bit versions of Firefox, or applications in general.