The mind is more than what the brain is doing. The idea isn't new, but it often gets too little respect. Perhaps because people think it implies something supernatural, or perhaps because it just seems weird, but it is a very respectable argument and in Alva Noe's hands, a powerful one.
We often take for granted in brain science that the mind is implemented by things happening inside the skull. That goes against the growing findings that perception is an active process of exploration that depends on our contact with the real world and the skills we possess for navigating its structure. This book takes on the significant challenge of bringing that difficult idea accessibly and non-technically into the popular mind and I think he does an excellent job.
Although Noe doesn't talk about it specifically, Ruth Millikan makes a good related argument that substance categories are really skills. We know substances by our skills for finding and identifying them over and over, not through their intrinsic properties. Noe approaches perception in much the same way. We know the world by interacting with it, not by (or in addition to?) simulating it with detailed models inside our head.
Noe goes a step further and points out how some concepts just don't make from a detached viewpoint, so we are often forced to destroy the phenomena of consciousness, reducing them to something else, in order to study them dispassionately. This is a tough sell, I think, to habitual materialists, but he doesn't rely too heavily on it.
The implication Noe emphasizes is that consciousness is a process involving interaction of the nervous system with the world, not (just) something that is lighting up inside our neural nets. The distinction is sometimes more subtle that Noe acknowledges. He approves of Gibson's ecological theory of perception, but doesn't address the equally important work on expectancy and hypothesis testing approaches to perception, such as Richard Gregory's ideas and the experimental work done around them.
He is probably right that much of our basic perception relies heavily on active engagement with the world, but then some of it, to me, clearly doesn't. He does a good job showing limits to the feature detection approach to vision (doesn't it beg the question to say that features are "built up" toward pictures in the brain?), but doesn't have an alternate explanation for the elaborate architecture of columns and receptor fields and their activity in dreaming and imagination that seem to support at least some version of the mental representation concept in some kinds of mental activity. It seems in places that Noe acknowledges this sort of work but considers it an impoverished-perceptual or non-perceptual kind of mental activity.
Other than the excellent writing and clear arguments, the best part of this book is the skillful use of various findings regarding phantom limbs, sensory illusions, and inattention phenomena to illustrate the empirical implications of a mind extended beyond the brain case. Even if you don't buy the full externalist argument in all its details, it's hard to read those examples and not have a little light go off in your head and think "oh, so that's what he means by the mind being outside the brain!" That's a mark of good writing.
Noe mentions but does not dwell on the role played by philosopher J Merleau-Ponty in many of these ideas, and his work is worth exploring as well. A good non-technical intro in keeping with the spirit of Noe's book is: Merleau-ponty: A Guide for the Perplexed (Guides for the Perplexed).
This book is a good read, a relatively quick read, and very thought provoking.