On Android an app can work as a "widget" that stays open on the desktop and can change to provide, for example, weather updates or other notifications. Windows has "Live Tiles," which change all the time -- either to show something informative, like an upcoming appointment -- or just for fun.
There's a little of this in iOS: Apps can display a number, typically to show unread messages. The Phone, Mail and Messages apps do this as well as some third-party apps, such as Facebook and Gmail. But that's as fancy as it gets, and it's far less sophisticated than on other mobile operating systems, compounding the Launcher problem in the second slide: The iOS desktop is flat and lifeless, and iOS's development restrictions don't allow modification of the desktop.