Tempering is a very important part of the harden & temper process.

The first reason for tempering is to minimize/eliminate quench-induced stresses. In fact, it is possible, in certain cases, to have a hardened but not yet tempered workpiece crack while under no strain whatsoever due to the level of stresses present after the quench.

The second reason is to adjust the hardness level to provide a measure of toughness/ductility. It is seldom recommended to select the highest attainable hardness as a working hardness in view of the negligible amount of stress relieved by such a low tempering temperature.

The third reason would be, in the case of highly alloyed steels, the elimination/reduction of an undesirable transformation by-product - retained austenite. It is possible, under strain, to have retained austenite transform to untempered martensite, a most brittle condition (example, the brittleness of a file). In this case, multiple tempers are recommended and in many cases, an increase in hardness will result after several tempering cycles. This will bring additional benefits such as dimensional stability and will provide the best toughness available for a given hardness level.