A Favicon Icon is an image that appears next to the name of your store on the computer tab. You can change this to your logo or any image you choose.
To find where to change this image navigate System > Configuration, and scroll to the General tab in the left-hand navigational column and select Design. Then expand the HTML Head tab.
Here you will see the options to upload a different image or delete the image altogether:
System > Cache Management
System > Index Management
Re-index if needed.