To be mindful is not the same as to be religious. This book crosses two already well-developed schools of thought, the scientific academy, and the religion of Buddhism, but as Wright points out, Buddhism isn't quite like other religions. Buddhism is defined by its absolute refusal to believe anything on conjecture—something that science shares. That doesn't mean that Buddhism is perfectly immune to conjecture—sometimes they resort to ideas like reincarnation to explain their point of view, but Wright feels we should put religious belief perfectly to the side to focus on the actual claims of the Buddhist faith.
By testing those claims, the author hopes to show that, actually, Buddhism is more like a school of philosophy which says simply that through extended meditation, people can experience higher states of consciousness and unlock powerful psychic clarity. He feels this is scientifically testable, and he explains his approach, ultimately concluding that, at least in these claims, Buddhism is literally correct, scientifically. It turns out that that's exactly what happens when someone meditates—their brain begins to function more successfully, and they report the same subjective claims that Buddhism makes.
There is another idea that Wright says science could verify about Buddhism: He feels that the teaching of no-self, or in Hindi, Anatman, which basically means that a person's mind can begin to perceive reality without respect for his own ego. This broad perspective makes Wright think of modularity of mind, which is the psychological idea that innate structures in our brains may be unlocked which serve evolutionarily developed functions.
He connects these two worlds, science and Buddhism, in one final way as well. He notices that many of the Buddhist teachings about the frame of a human life (that we are born from parents), and the idea that our consciousness is made of a community—these ideas are shared with evolutionary psychology and evolutionary biology, if one says that our consciousness is the product of evolution, then that might explain what the Buddhist scriptures are teaching—simply to observe one's instincts.