The article, which largely focused on the neuroscience research, makes the distinction between two types of meditation: 'focused attention' meditation - that involves focusing on a particular thing and refocusing if you become distracted by thoughts or sensations; and 'open monitoring' meditation which involves nonreactively monitoring the content of experience and acting as almost a detached observer to feelings and mental events.
It has also been found that compassion meditation increases feelings of empathy with the suffering of others.
My current audio book is all about this. It is called The Science of Enlightenment by an American Buddhist called Shinzen Young. This must be a compilation of recordings of talks he has given, because you can hear the audience occasionally. It's actually about the science of meditation, and similar practices, in a range of religious and non-religious traditions, including hypnotic trance, and his experiences of changes in mental state and concentration. I have listened to about 2-3 hours so far and I am finding it very rewarding. I think he presents the facts in quite a pragmatic and non-dogmatic way. I wouldn't seek to defend every point he makes but overall I have found it helpful and convincing.
One anecdote he tells is about coming off thyroid supplements (his thyroid has been removed) as part of a medical experiment. His IQ dropped to the brink of dementia, and he was commenting on what this change in cognitive ability felt like, and what it did to his sense of self. A very poignant story. Of course people with real dementia can't come back from that brink, they must go over it.