From Wikipedia:

A favicon (short for favorites icon), also known as a website icon, page icon or urlicon, is an icon associated with a particular website or webpage. A web designer can create such icons in several ways and many recent web browsers can then make use of them. Browsers that support them may display them in the browser’s URL bar, next to the site’s name in lists of bookmarks, and next to the page’s title in a tabbed document interface. Some operating systems will also often use the favicon for Internet shortcuts to sites placed on the desktop or in other directories.

You can easily add a favicon to your Drupal site by going to the theme settings page: Administer > Themes > name-of-theme – the clean URL of the theme settings is admin/build/themes/settings/name-of-the-theme. Please replace “name-of-theme” with the name of the theme you are using.

Once you are on the theme settings page for the theme that you are using you can add your favicon in the “Shortcut icon settings” section midway down the page. Using the “Upload icon image” form you can select a image on your hard drive and upload it to your Drupal web site. Don’t forget to click the “Save configuration” button at the bottom of the theme settings page.