You may have clicked on the icon in the disc image.
http://www.mozilla.org/products/firefox/releases/1.0.6.html#othersystemsMac OS X
Once you have downloaded the Firefox 1.0.6.dmg file, double click the Firefox Disk Image to open it in Finder, and then drag the Firefox application onto your hard disk. Drag the icon to your Dock if you want it to appear there.
For Firefox 1.0, double click the Firefox 1.0.dmg.gz Disk Image to uncompress and mount it. Your browser may have already done this for you. Double click the Firefox Disk Image to open it in Finder and drag the Firefox application onto your hard disk. Do not double click the icon in the disk image! Be sure to drag the Firefox application out of the disk image and onto your Hard Disk before running it. Drag the icon to your Dock if you want it to appear there.
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# Do NOT run Firefox from the Disk Image! - doing this will cause an infinite restart loop (the symptom of which is a Firefox icon that bounces briefly in the Dock then disappears and reappears, bounces and disappears, over and over). To break Firefox out of this loop, open a Terminal and type "killall firefox-bin" and press enter. Install Firefox to a location you have write access to and try again. When installing on a multi- user limited access system, install it into a shared location as administrator, run it once and then all users should be able to access it.
# If Firefox does not display a browser window, quit Firefox using Cmd+Q and open ~/Library/Application Support/Firefox/Profiles/<garble>.default/ and remove localstore.rdf. Restart Firefox. Any toolbar customizations you have made or window placement will be lost.
Hope this helps. A mac using friend of mine had weird issues initially with Firefox. He got squared away and LOVES Firefox now.