Steel (iron alloy (Fe) with carbon (C)) without any special heat treatment, simply cooled after forging on the open air is soft. A knife made like this can bend in your hands. Before our ancestors had learned how to heat-treat steel, they forged it without any heat. Cold-hardened steel is strong, and hard. A knife, or a sword so treated bent less than the competition’s crafts, cutting tools from copper or bronze. It was better! Someone noticed, however, that as soon as the red steel cools down in the water after being forged, it becomes extremely hard, cutting the competition who hardened by the cold. There have been attempts since then to normalise the process: hot steel must be of the right colour (sunset at a certain time of the year!), water must be of the right temperature (cool but not too cold), water from the mountain stream is better than from the river, the addition of urine makes it harder, etc. Now we know what happens during hardening, we have tools to standardize the process of hardening steel. Hardening in two different corners of the world of steel of the same type (even from different manufacturers) should have similar effects.
Hardened steel can be several dozen times stronger than unhardened steel. Hardened steel can be used for cutting (or peeling with a knife) non-hardened steel. An argument for knife lovers: after hardening we can achieve the hardness of over 60HRC, we get high resistance to bending, the knife will get less sharp long!
Hardening is a complex of operations in common language: Heating the steel to the right temperature (depending on the steel type), heating it at this temperature: Austenitization (then the steel "shines", higher up 760O C) and cooling it down sufficiently quickly: Extinguishing (in water, oil, compressed gas, air).
When heated to such a high temperature, the structure of the steel changes and the Carbides contained in it dissolve (Carbon is transferred to the steel, as are the Alloying Compounds and Admixtures contained in it). When heating steel (Austenitization) at high temperature, the concentration of carbon and elements contained in the steel (Admixture, Alloying Components) in the entire volume of the tool is compensated for. During rapid cooling (extinguishing), the structure of the steel changes again, the components (coal, other elements) are "frozen" in the steel, reinforcing it. Simple, isn’t it...?