That's just the icon, I think. Tap on it and it should take you to the app to set it up. Or if it's a widget, long press on the screen and choose widgets, the scroll until you find the widget you want and long press it for it too appear on the desktop.
If it is the actually app/widget, long press on it and a resize option will appear.
Right. The "apps" are just shortcuts to open a specific app. Widgets are areas of the screen that actively update and interact with you as if they were apps.
So an "app" (shortcut) on your home screen for a weather service will open up the weather app when tapped. A widget for that same weather app will show you the weather right on your home screen.