"greater sensitivity" refers to being more aware or responsive to something. It means having a heightened ability to perceive or understand things with more detail and accuracy. Full definition
This movie considers with great sensitivity many politically correct topics without supporting the politically correct conclusions. (firstthings.com)
Early developmental stages appear to be the period of greatest sensitivity to its effects, and some studies have linked prenatal exposure to later physical and neurological difficulties. (ournourishingroots.com)
The breastfeeding mothers, on average, had higher activity in the parts of their brains linked to nurturing behaviors and showed greater sensitivity to their babies when seen again at four months postpartum. (breastfeedingtoday-llli.org)