A FavIcon is a small 16 x 16 pixel graphic icon located in the URL address bar of your browser.

A website designer creates the small icon by loading a small picture into a generator app found on a website.

The generator app we like to use can be found here...A website that generates your favicon.

Placement

The favicon can be used in a number of other places, as a desktop icon, next to the page name in a list of bookmarks.

To summarise 

You can read more indepth information about the history, developement and browser support of the favicon at the following address, https://en.wikipedia.org/wiki/Favicon