This is such a simple plugin that it begs the question why isn’t this built-in to WordPress already? Here’s what the author says:
Admin Favicon is a very simple plugin. It creates a link to a shortcut icon, or favicon, into the header of the WordPress administrative console. What does this mean? Look at the address bar or tab indicator of your web browser. You should see an image next to the URL of this page. This is a favicon. It lets you easily identify this page from other pages you have open. This is very valuable for tabbed browsing, when you have many tabs open at the same time.
It would be even better if you didn’t have to manually enter the favicon’s URL.
Homepage Admin Favicon