UIScene concept is not clear
The biggest thing is that scenes set up multiple window support (currently only available on iPadOS and macOS). It is also useful for SwiftUI setup on iOS.
The SceneDelegate controls what is displayed on the screen "to manage life-cycle events in one instance of your app's user interface.", while the AppDelegate controls your entire app life-cycle.
You'll also notice keyWindow no longer exists for iOS. It's quite possible multiple window support is coming to iOS, but this is speculation right now.
Hopefully this clarifies things a bit and gives you an idea of why Apple is updating the implementation.
This article gives some more data regarding SceneDelegate that you may find useful: https://www.donnywals.com/understanding-the-ios-13-scene-delegate/
The documentation
You should read the App and Environment Article from Apple instead of UIScene documentation.
Explaination
As it says about the scenes:
Scene, Manage multiple instances of your app’s UI simultaneously, and direct resources to the appropriate instance of your UI.
We had only one scene back then before iOS 13, So the only thing we need to run ViewControllers simultaneously was multiple Windows on top of each other. But now, each application can have multiple instances running at the same time! Each scene has its own state and it might be in the foreground while others are in the background or are suspended, while Window was completely depended on the application itself.
Imagine we have 2 view controllers (consider there are no scenes) running on the left and right side of the device and then we need to show a banner. Using the old window method will show the banner on both of them! And if you need to pick one, you may end up finding the correct controller and presenting the banner on it, (I think all of us done this method before getting familiar with UIWindow)
So apple introduced Scene, a container for each separate instance of the app. So you can manage each one separately and each of them acts like a separate app. It has its own windows and controllers. But all of them are managed by a single object, UIApplication.shared and it has a delegate to handle general events (usually from outside of the app) and entire application life cycle.