When 3D Touch launched alongside iOS 9 and the iPhone 6s, part of the promise was quick shortcuts to some of the most used functions in apps. With iOS 10, people may sometimes be able to skip opening apps entirely.
In the new OS, pressing down on a home screen icon will reveal not just Quick Action shortcuts but a widget with handy information. With Calendar for example, this translates to upcoming events. Weather will, of course, display the day's forecast.
Perhaps one of the better uses of the technology at the moment is the Activity app for the Apple Watch. Its widget lets users see daily Move, Exercise, and Stand figures all at once, which like the Weather widget accomplishes one of the app's primary tasks without it being launched.
Some widgets are essentially even more direct shortcuts, like the one for News, which highlights recent headlines and lets you jump straight to them. In the same way, a Photos Memories widget can be used to hop straight into a collection.
Essentially the widgets are the same sort that appear in iOS 9's Notification Center — or in iOS 10's lockscreen and Siri search. They're important not just for their convenience on the home screen, but because they also have "Add Widget" buttons making it easy to add content to the lockscreen and Siri search.
There doesn't (yet) appear to be any third-party support for 3D Touch widgets, likely because developers will need to update their apps to include widgets in 3D Touch support. It's likely that apps will begin seeing home screen 3D Touch widget support when iOS 10 launches this fall.