The favicon shows up in your bookmarks, in the address bar, and on the tabs of loaded pages in a tabbable-browser. Being able to dynamically switch the favicon on a page promotes the favicon to the ability to be used as a "Status Monitor" of a webpage. For example, I am uploading a bunch of files to a website, the favicon can show an "uploading" icon, and then a green "complete" icon when it's done. I can then return to the page to carry on whatever I was doing now that the upload is complete.
Or perhaps I have a webpage open to my weblog stats, or server statistics. The color of the icon can be updated to alert me to notifications and messages. A news site could change the icon when there is a new and pertinent story that I may want to read.