“Breadth of mind” usually means “ability to see an issue from a wide variety of viewpoints.” In contrast, a “narrow minded” person has a very rigid way of looking at the world and cannot understand that other people have different opinions and beliefs. The gist of the sentence is that, as people get older, they often become better able to understand and appreciate different people’s opinions and beliefs. The part about “provided the brain is health” is a little hard to understand; maybe the author means “provided that the person is not suffering from some sort of mental illness or disability that prevents it.”