Favicon
Favicon also known as a website icon, url icon, or bookmark icon. Generally it is your website logo or some other small graphic which is used as favicon. This favicon is displayed in address bar or page tabs when u load any websites. A web designer can create such an favicon and put it into a website. This favicon is also see in the bookmarks.

Creating Icons Favicon image
A favicon must be square in size, and at least 16 x 16 pixels. Consider creating both a 16 x 16-pixel icon as well as a 32 x 32-pixel icon. To create the icon, use an any image editor such photoshop, and save the icon in the .ico file format. Explorer will ignore icons that are not in .ico format, and will instead display the default shortcut icon of the browser.

You can use online tool to generate the favicon.
    http://tools.dynamicdrive.com/favicon/

Including Favicon
You can include this favicon in the root folder of the website and just write small html code in the head section of the HTML document. And the favicon will be displayed in the address bar.

<link rel="icon" type="image/x-icon" href="/favicon.ico">

In case of joomla website, there are components for including or changing the favicon for you, just install these joomla components. Go to that component, select image to be converted as favicon and its done.

Components available for favicon are:
http://www.phoca.cz/phocafavicon/