Kerf is defined as the width of material that is removed by a cutting process. It was originally used to describe how much wood was removed by a saw, because the teeth on a saw are bent to the side, so that they remove more material than the width of the saw blade itself, preventing the blade from getting stuck in the wood.
When talking about CNC shape cutting with typical cutting processes, kerf is the width of material that the process removes as it cuts through the plate.
Over the years I’ve heard some people use the term when referring to the angle on the edge of the part, but that would be an incorrect use of the word. The “cut angle” on the edge of the part makes measuring the kerf width sorta tricky, but for consistency, the word “kerf” should only be used when talking about the actual cut width.
When cutting parts on a CNC plasma or laser machine, you want to produce accurate cut parts, with final dimensions as close as possible to the programmed shape. So if you program a 6” by 6” square, and the plasma arc removes 0.200” of material, as it cuts, then the resulting part is going to be 5.8” by 5.8”. So the actual tool path has to be compensated by 0.100” to the side of the programmed path, all the way around the part.
Rather than re-program the part at a different dimension, the CNC will take care of this automatically just by telling it which direction to offset, and by how much. Most modern CNCs take the actual kerf amount and automatically offset the tool path by 1/2 of that amount, so that the finished part comes out very close to the programmed dimensions. That is why the kerf value is often referred to as “kerf offset”.