AppKit is Apple's framework, a library that is part of the operating system, for building the graphical, event-driven user interface of macOS apps. Apple's documentation lists it from macOS 10.0, and it is also available to iPad apps brought to the Mac with Mac Catalyst. Code that uses it is written in Swift or Objective-C.
AppKit contains the objects that draw windows, panels, buttons, text fields and other views, and it handles the events between the app, the person and macOS, such as mouse, keyboard and trackpad input, menus, the Dock, gestures and drag and drop. It also handles printing, animation, documents, text layout with TextKit, fonts, color and accessibility, with built-in support for localization. AppKit works with SwiftUI, Apple's newer declarative interface framework: AppKit views and view controllers can be placed inside SwiftUI views, and SwiftUI views inside AppKit, so one app can mix both.
AppKit has no separate price. A free Apple developer account allows testing apps on one's own devices with Xcode; distributing apps requires the paid Apple Developer Program.