To backup or transfer your Firefox bookmarks to another computer using Mac OS X Leopard follow these steps:
Step One Open a new Finder window by clicking its icon in the dock.
Step Two Select Go : Go to Folder from the Finder menu.
Step Three Enter ~/Library/Application Support/Firefox/Profiles/ into the textfield and then click the Go button.
Step Four You will see a folder in the Finder window with a randomly generated name. It might look something like zy27vs1x.default. Double click this folder to open it.
Step Five Locate the bookmarks.html file in the Finder window. Copy it to a different location for backup. If you want to move your bookmarks to a different computer then copy and paste the bookmarks.html file to the exact same location on the other computer.
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It looks like this information is out of date. I found the file. But the last time bookmarks.html was updated was 4 years ago. So this appears to be an abandoned file by newer versions of Firefox. I am using 43.0.4 in January 2016.
If it's installed on your System, it would be in the Library folder of your home directory, i.e. /Users//Library/Firefox.
You many need to make your Library folder visible in order to see it though.