Describes a person, sense, or reaction that is quick to notice or respond to stimuli, changes, or subtle cues. Can be used positively (keen awareness) or negatively (easily affected).
彼は音に敏感で、小さな物音でも目が覚める。
He is sensitive to sounds and wakes up at the slightest noise.
My skin is sensitive, so I'm careful when trying new cosmetics.
She is sensitive to trends.
This machine reacts sensitively to changes in temperature.
During pregnancy, one becomes sensitive to smells.
That is a politically sensitive issue.
敏感 is an adjective describing someone as easily affected or reactive, whereas 感受性 is the noun naming that underlying capacity.
敏感 describes being quick to react or perceive (e.g. to stimuli or criticism), while 繊細 describes a delicate, easily-affected inner sensitivity or fineness of form.