Knife sharpening -- why does it work?

It seems intuitively obvious that pushing a knife or other sharp implement blade-first into an object harder than itself would dull the blade, not sharpen it. So how come “cutting into” a knife sharpening rod sharpens the knife?

The same way a pencil sharpener sharpens a pencil. Here, take a look at one. Notice how the blade sits at an angle? You need to slightly angle the knife when you rub it against a shapening rod or stone so that the roughness of the dull knife is abraded and we are left with a sharper knife.

There are two things that people do that “sharpen” blades. One is to truly sharpen - that is to remove some of the knife’s material. The other is to “hone” that bade - that is to bring the sharpest part of the blade back to the right shape.

The two most common things that make a knife cut less effectively, and how they are corrected:
1.) The blade of the knife is worn down from a sharp point to a dull bump. Think of the tip of a pencil after you’ve been using it. The carbon gets rounded. The only way to bring back the sharpness is to remove some of the material all around it (ala a pencil sharpener, like Patty O’Furniture said). This is usually done with stone of some kind (e.g. a sharpening stone, a sharpening wheel, or the sand of a band sharpener.) By keeping the blade at the right angle, you remove the excess material. See this blade? When you are running a blade over a stone, you are (hopefully) removing just enough to reform the very tip. Speaking from experience, it’s tricky to get just right. You need to keep the angle very constant. It’s like trying to sharpen a pencil with a swiss-army knife. You might get something that works, but it will never look as pretty as using a guide.

2.) The blade of the knife gets small bends that keep the sharp part from cutting. Try this: put your hands palms together with fingers pointing up. Now push with the tips of your fingers on your right hand, so that the fingers of both hands bend. That’s being “out of true.” This is corrected with a piece of steel that simply brings the sharp part back into alignment. Ideally, this is done every time you use your knife. If you hone often, you can easily get away with infrequent (once every other year or so) sharpenings.

Both of the corrections are assuming non-serrated knives. Serrated knives are beyond me in repair and upkeep.