Game Engine Programming involves creating the software framework that allows developers to build and run video games. This includes designing systems for graphics, physics, sound, and user input, enabling the game to function smoothly and efficiently. Developers use various programming languages, such as C++ or C#, to implement these systems. Popular game engines like Unity and Unreal Engine provide tools and libraries that simplify the development process, allowing creators to focus on game design and storytelling rather than low-level programming tasks.