What? Favicons are the little pictures that appear in your bookmark list, at least most of the time, and sometimes in toolbars and tabs depending upon your browser. They are intended to help you find what you want more quickly, which I think they do quite well.
If you look at my toolbar, pictured below, you will see a load of favicons that enable me to access my favourite sites quickly. Look carefully and you will see that some have a blank document image instead of their own icon, which can happen if there is no icon file or the browser cannot find one. If all were blank it would be a lot harder to find what I want quickly.
Favicons are small image files, typically 16×16 in size, with an extension of ICO. They were originally implemented in Interner Explorer 6, which looked for a file named favicon.ico in the root directory of any website and this still where they are commonly found. Although later browsers can support files that are larger and located elsewhere, for maximum compatability, it is best to stick with the initial approach.
My favicon is from the picture that is used as the banner for this site. With Photoshop Elements I removed the background leaves and reduced the size to 16×16, then saved it as a PNG file. Finally, as the file must use the Microsoft ICO format, not supported by PSE (at least on the Mac), I converted it using Preview. Frustratingly, iWeb does not support favicons so I have to upload it to my web host after each republish.
A good icon can be used elsewhere to improve the branding of your site so it is worth taking some time to set one up. Getfavicon is a good site to learn more about favicons, get advice for creating your own and extract the favicon from sites that don’t use the default file name and location.
EDIT: I should mention that this site, WordPress, automatically generates a favicon from a larger image that you upload (or a default, randomly generated pattern that has been assigned to you). I need to update the original image so that the favicon appears as I intend.