- The obvious is the favicon it will add in web browsers.
- The big more important reason is when someone is on your site and chooses add to home screen, that icon is placed on the mobile home-screen. Rounded corners will help it look and feel just like a mobile web app. This makes it really easy for someone to launch your site right from their home-screen.
Since your site icon has the chance to be along side Dropbox, Google and other popular apps, you want to have your site icon look just as good as the other app icons.