The gerber files are the files needed for the manufacturers of the board to build your board. The CAD is the program which you can use to create your boards and from them create the gerber data.
Programs like PROTEL allows you to create a PCB and correlate it to a schematic. That way you know if what you have drawn in your schematic is all "wired" in the PCB. After you are done, you generate gerber files from the CAD program.
What the program does, it creates a file for each layer of your PCB, so that the manufacturer knows where to put each layer afterwards like a sandwhich.
Hope it helps.
Ivan