The favicon is pretty much normality these day. the interesting bit here is the apple-touch-icon which is used if you save a bookmark to your home screen on an apple touch device such as an iPad or iPhone. Interestingly enough, android also supports its usage. As far as I can tell, the apple-touch-icon size is 60px by 60px. As the comment says, if your icons are in the root of your domain, these links aren’t required.

<!-- Place favicon.ico and apple-touch-icon.png in the root of your domain and delete these references -->
<link rel="shortcut icon" href="/favicon.ico">
<link rel="apple-touch-icon" href="/apple-touch-icon.png">