A favicon (short for "favorites icon") is an icon associated with a website or webpage intended to be used when you bookmark the web page. Web browsers use them in the URL bar, on tabs, and elsewhere to help identify a website visually.
A favicon is typically a graphic 16 x 16 pixels square and is saved as favicon.ico in the root directory of your server. You can use a favicon with any WordPress blog on a web server that allows access to the root directories.
A favicon can be created using any graphics/image editing software, such as GIMP, that allows the saving of .ico files. There are also online services that will allow you to create a favicon for free.
The image should be clear and is usually designed to match your blog's image and/or content, a big task for something so small.
To prepare the image to be saved as favicon.ico:
By cropping or adding space around the image, make the image square.
Resize the image to 16 x 16 pixels.
Save the file as favicon.ico.
If you're using an online service to create your favicon, such as FaviconICO.org (creates 24bit favicon.ico with a transparent background, follow the instructions provided by the site and then download the favicon.ico image to your computer.