Toughness is the ability to absorb energy without fracture. (I called Larrin and gave me this definition) In use knives that are too soft will roll at the edge rendering them useless, and knives that are too hard will chip out at the edge or worse break all together and become useless. Proper heat treating is the best way to ensure the best balance of hardness and toughness.
Good toughness in properly heat treated steels will affect other things like edge stability, edge holding, and the sharpenability of the knife. To increase both the toughness and hardness of the steel correct forging and heat treating cycles must be used.
The amount of carbide in the steel and the size of those carbides along with the over all hardness of the steel has the biggest effect on toughness. Some elements added to steels will increase toughness.
Grains in steel are like soap bubbles in a jar. Grains are different than carbides. The smaller the grain and the smaller the carbides in the steel the tougher the steel will be. Correct forging and heat treating of the steel allows proper grain refinement and to a lesser extent smaller carbide size.
Powder metalurgy steels were developed to be able to increase both wear resistance and toughness by reducing both the grain size and the carbide size and by more even distribution of the carbides in the steel.
More to come.