If steel cools from a high temperature to cold in a short period, the metal becomes very hard, but brittle. Conversely, if it is cooled slowly, it becomes softer and suppler. Samurai swords were used primarily as a slicing weapon, so the blades were subjected to severe shock upon impact. It a blade was brittle, it might shatter on contact. However, if it was made too supple, it would not hold an edge. This created a dilemma for the sword makers.
Japanese samurai sword makers discovered that by painting a thin layer of a clay formula onto the cutting edge, and a thicker layer onto the back the blade, before cooling the blade, the steel would have a hard cutting edge but a supple back. Because of the different speeds at which the two areas of the steel cooled, the blade developed a natural curve that the sword makers then worked to create the famous curved blade of the samurai swords.