When talking about a school it means things like, do they notice a pupil who is unhappy and would they know what to do about it, do they clamp down on bullying and help pupils to resolve their differences, do they have procedures in place to support a pupil who is struggling due to problems at home/illness/bereavement/etc
if it is good it can be far more than just everyday basic care: dd's school, for instance, has a counsellor who is specially trained in bereavement counselling