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).
He is sensitive to sounds and wakes up at the slightest noise.
肌が敏感なので、新しい化粧品を使うときは注意している。
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.