Your app icon is a very important graphical asset. It's typically how users will start your app on their mobile devices. As such, it has to be easily distinguished from the other icons on the user's screen. For a game or a highly graphical app, the icon might be a more literal representation of the app itself. But for many other apps, the icon is an abstract representation. If your app has a recognizable brand, the icon can be a play off the brand, such as the app icons for Facebook, Twitter, and the like.
Each platform your app supports will have different physical requirements for your icon. But in most cases, the aesthetic is largely the same across platforms and the only difference is the size and whether or not there are rounded corners (and to what degree). In many ways, this makes designing a cross-platform icon fairly easy. It isn't difficult to target all the various sizes as long as you avoid the corners. This isn't to say that your icon must be identical across...