If you have a cat or if you are thinking about getting a cat, the reality is they will scratch. In fact, cats need to scratch — it's really that simple.
Scratching is a behavior that is instinctive for cats much in the same way that using a kitty litter box is. You don't need to teach a cat to use the kitty litter box, they just will. When it comes to scratching, while you don't need to teach them to do this, you certainly cannot teach them *not* to do this. Cats will scratch.
Cats scratch, like many other animals, to mark their territory. Obviously, scratch marks are a visual sign but beyond what your eyes can see, there are also scents that are left when the cats scratch. Unless you have a very strong sense of smell, which we humans don't have, you won't be able to smell the scent left by the cats but other animals can and do. Below the cat's paws are some superficial glands, which secrete the pheromones.
In addition to leaving a scent or marking their territory, scratching also acts like a nail file removing the dead cells from the claws. More than likely, scratching also helps to strengthen the paws and forearms. It seems to me that cats ultimately just enjoying scratching.
Cats usually scratch around important areas that mark their territory such as near windows, sleeping areas, the kitty litter, etc. As a result, it's always a good idea to put scratch pads near important areas. In fact, recently, I noticed one of my cats scratching the table where I work. I didn't realize the significance of why my cat why was scratching the table until I really thought about it — it's an important location to my cat.