A favicon is a site specific favourites / bookmark icon created by a site owner that will be saved on a visitors own bookmark / favourites list, if they choose to add the site to their bookmarks / favourites. It is a chance to familiarise your visitors with your brand even when they are away from your site.
Using an art package like Adobe Photoshop, PaintShop Pro or GIMP.
Create an image 16X16 pixels in size. Due to the size you should use as few colours as possible.
Save the image as an ICO file under the filename of favicon.ico
Upload the file via your FTP client or File Manager within the 123-reg Control Panel
Place the file in your root directory (the same one containing your website index / front page)
It may take up to 24 hours for the file to propogate. Once successful you will find the icon showing alongside your website when you bookmark it / set it as a favourite.