A CNC router is a machine that cuts and engraves designs on materials such as wood, plastic, foam , or steel. The controller of the machine reads in a design produced on a CAD program and in this way controls the cutting. Once your 3d design is finished on the program, it is transferred to a toolpath program (such as AutoCad), where the software sends the exact cutting directions to router.
The linear drive system of the machine moves across the supplied material on the X (front to back), Y (left to right), and Z (up and down) axes. The cutting board hold the given material while the spindle of the router makes the various cuts and engravings by rotating the cutting tool and controlling the speed. There are different types of cutting boards, such as the t-slot, which can hold different types of material but is less efficient, and the vacuum table which only holds flat materials. The linear drive system on each axis, consisting of a motor, linear bearing system, and lead screw assembly, moves the spindle to the correct position. The motor is the connecting piece between the controller and the spindle.
Here is a tutorial that goes through the entire process from creating a design in a CAD to creating it on the CNC router:
http://www.cnccookbook.com/MakeCNCParts/HowToMakeCNCParts.html
Here is a video with examples of objects created with the CNC router: