Favicons are small images that appear right next to your site's URL in the web browser and in your favourites list. How to apply your Joomla site a decent favicon?
If the favicon won't appear, make sure that you have a referral to your favicon.ico file in your template's index.php file's head section. Somewhere inbetween your <head> </head> tags should be a code:
<link href="/templates/yourtemplatename/favicon.ico" rel="shortcut icon" type="image/vnd.microsoft.icon" />