Weirdly, there's never been a 64-bit version of Firefox until now. But if you're running Windows 7 or later, you can now explore the internet with the browser while using twice its current 32 bits. Making use of the full 64 bits will allow the software to capitalise on the assets of modern processors. It won't necessarily run faster, but you should find that many web apps run better (or at all!), and the browser's security should be stronger, too.
It worth noting that Mozilla's Mark Mayo points out that "Firefox 64-bit for Windows, by design, has limited support for plugins and users will notice that certain sites requiring plugins that worked in previous 32-bit versions of Firefox might not work in this 64-bit version."
Image by Thanh Nguyen under Creative Commons licence