The "Favicon" means "Favorite Icon."

It refers to the customized icon that appears in the browser title bar when you are surfing on a site.

It is a 16x16 pixel graphic with the name favicon.ico.

In Joomla 1.5, put your favicon.ico file in the root folder of your template.  So, for example, if you are using the ja_purity template, it would go into /templates/ja_purity.

The easiest way to make a favicon is to use one of the webbased favicon generators.   I like to use the free one provided by Dynamic Drive:  http://tools.dynamicdrive.com/favicon/.