CNC Machining is Computerized Numerical Control Machining.
The Numerical Control process is a way of moving various components in a system in a synchronized way that results in a specific action or part being created. When motion is combined with a working piece, such as a milling bit, it can remove material to form a specific shape. Similarly, it could have a working head that layers material in a specific way so as to form a part. The removal form is called subtractive machining. The creation of a part via adding layers is additive machining.
Numerical control was originally developed using cams, like a camshaft in a car engine, to pull levels, move pulleys, or any other mechanical linkage that could be driven by the cam. When electricity became available, the process moved to include electrical options. In the 1940's and 1950's, the electrical variations were heavily used in manufacturing processes. Cams were replaced with electrical devices that could store larger, more complex instructions. The machines would be built out with a number of very specific functions using logic circuits, relays, motors, and screws. The control unit would read in an instruction set, then use the prebuilt functions in the hardware to perform the function that was read off the storage media. Numerical Control refers to the last evolution to that progression.
When computers began entering industry, they replaced the control unit and hardcoded circuits. This allowed for simplified hardware and also allowed the control system to read in mathematical models and execute steps and actions based on the model rather than having to define each specific step in a linear fashion. Also, it allows newer functions to be defined in software, rather than hardware.