Fireclam is a Firefox add-on which uses ClamAV to automatically scan Firefox downloads for viruses.
This download only gets you the Firefox extension, so you must download and install ClamAV (Linux, OS X) or ClamWin (Windows) first. (If you forget, then Firefox won't be able to download anything as Fireclam will complain that ClamAV can't be launched.)
Once Fireclam is installed, it waits for any downloads to complete, then runs ClamAV to check them. You'll see this happen under Windows as a command window appears, and there will be a brief delay - typically just 3 or 4 seconds - while ClamAV examines the file.
If your download is found to be safe, then nothing more will happen. There's no "all clear" message, no smiley face icons or anything else, you just carry on and work with the download as normal.
If a threat is detected, then an alert dialog pops up to warn you. By default, this report is all you get, and so you'll have to delete the file yourself. If you'd prefer any dangerous downloads to be deleted or quarantined automatically then you'll need to set this up from ClamAV (Tools > Preferences).
To see how this works in practice, try downloading the EICAR test "virus". It's just a text string, not a real threat, so can't hurt your PC, but it should be enough for you to see ClamAV's warning in action.