Generally means “responsiveness to a perturbation”.
E.g.:
sensitivity (model variance) … responsiveness of a model’s output to changes in its input features.
fisher information … responsiveness of a model’s likelihood to changes in its parameters.
derivative … rate of change of a function with respect to its input… which of course ties this to a lot of other contexts where you might hear sensitivity, like Monte Carlo Gradient Estimation in Machine Learning
…
Tho of course there are cases where this generalization/name does not fit at all:
sensitivity (statistics) … true positive rate; ability of a test to correctly identify positives. How sensitive the test reacts when the condition/signal is present. (detection abililty)