Key process input variables are process inputs that have a significant impact on the variation found in a key process output variable. That is, if the key process input variables were controlled (e.g. held constant), the process would produce predictable and consistent outputs.
For example, if the flatness of a clutch disk has a significant impact on the slip torque of an actuator, then clutch disk flatness would be a key process input variable.
As another example, my wife likes to experiment with baking the healthiest cookies possible by substituting fat free yogurt for butter. Clearly, the absence of butter has a large impact on the consistency and taste of the cookies. By finding an acceptable butter/yogurt mix and then holding this key process input variable constant, I should expect consistent cookie consistency!