Firefox on Debian is supplied in the ESR Extended Support Release which gets only a few updates and you have to wait long for anything new to be implemented.

If you want to switch to the most recent Firefox version and not the included Firefox ESR, you can do it like this:

Go to your root shell in Debian / Linux and  type this:

This will create the folder, do a backup of the ESR release and alter the linked version
mkdir /opt/firefox
mv /usr/lib/firefox-esr/firefox-esr /usr/lib/firefox-esr/firefox-esr_orig
ln -s /opt/firefox/firefox/firefox /usr/lib/firefox-esr/firefox-esr

to download and update firefox to the newest release you can do this:
wget -O FirefoxSetup.tar.bz2 “https://download.mozilla.org/?product=firefox-latest&os=linux64&lang=en-US”
tar xjf FirefoxSetup.tar.bz2 -C /opt/firefox/

to restore to the old ESR version you can do this:
unlink /usr/lib/firefox-esr/firefox-esr
mv /usr/lib/firefox-esr/firefox-esr_orig /usr/lib/firefox-esr/firefox-esr

Happy Browsing 🙂