UIKit is Apple's framework, a library of ready-made classes, for building the graphical, event-driven user interface of iOS, iPadOS and tvOS apps. It provides the window and view structure of an app, the delivery of Multi-Touch and other input, and the main run loop that manages interactions between the user, the system and the app.
UIKit apps follow the Model-View-Controller (MVC) design pattern: model objects hold the data, view objects show it, and controller objects move data between them. UIView displays content and UIViewController manages a view; UINavigationController and UITabBarController implement common screen designs, and UITableView and UICollectionView show long lists and grids. Controls such as UIButton and UISlider, and gesture recognizers, handle input. Apps are built in Xcode, Apple's development tool, from template projects, and UIKit views can be mixed with SwiftUI views in one app.
UIKit has no separate price. Registering as an Apple developer is free; advanced app capabilities and app distribution require a paid Apple Developer Program membership.