Apple's iOS 14 update sports an entirely new way of organizing apps using the new "App Library" feature. The App Library is designed to systemize large collections of apps and make them easier to access, without any initial effort from the user.
The biggest benefit is cleaning out all those pages of apps you don't want to delete, but also don't need to see day to day. That way you can setup your iOS 14 Home Screen just way you want.
All apps are automatically added to the App Library, and the area can be found by swiping on the home screen all the way from right to left. In the App Library, all apps are organized into folders titled Social, Utilities, Productivity & Finance, Information & Reading, Creativity, Other, Health & Fitness, Shopping & Food, Entertainment, Travel, Games, Arcade, and Education.
There is no way to change the organization of the folders because it is automatic. Each folder displays three suggested apps along with a collection of four smaller app icons that you can tap on to see all of the other apps in that particular folder.
You can search to find a specific app in the App Library by pulling down and typing the name of the app. There is also a "Suggestions" folder which makes app recommendations based on usage habits, and a "Recently Added" folder to make it easy to find your newest apps.
The three apps in each folder are intelligently surfaced based upon what may be most useful at a given time. Users can even choose to limit how many home screen pages are displayed in order to gain quicker access to the App Library.
Long pressing on the main App Library page causes the apps to jiggle, letting apps be deleted directly from the App Library. Alternatively, you can also long press on any app icon and select the "Delete app" option.
When you download a new app on your iPhone, you can actually have it moved straight to the App Library and the relevant app category, instead of it appearing on the home screen, by selecting "Show in App Library" in Settings.
You can still organize apps as you wish on other screens, dragging apps to your desired location and using folders, but the App Library makes for a much more organic and organized iPhone interface.
Update: The App Library has facilitated a new trend of customizing the home screen and changing app icons using Shortcuts. Without the App Library, apps with custom shortcut icons would be duplicates, with no way of hiding the original app. Thanks to the App Library, the original app can be hidden away from the home screen.