The idea: Society is a vertically organized enterprise. Different concepts are used to attempt to implement a sort of control over others; the control of language, and of grammar itself, could be considered a type of imperialism...to paraphrase, there's no quicker way to implement a sort of control over a group of people than to ensure that they cannot have a voice within a society without adhering to strictly delineated guideline regarding how to write/how to speak. In response to the vertically oriented, top-down society, a "nomad" thought emerges in response, one that refuses to settle down within the predominant format, one that chooses to countermand the society. The development of a counter-reactive force to society, however, a society that attempts to eradicate "nomad thought", thought that does not organize into hierarchies and the idea of the have and the have-not, requires a "rhizomatic" form of connection. Imagine a set of differentiated cells that, rather than resting on a vertical plane, are organized horizontally, with the formation of different shapes, different types of conformities that help upend the tyranny of the dominant language, the dominant order. The rhizome is a dendrite that allows the players and actors in this philosophical field to connect outside the field of the hierarchy, in a way that could be more effectual than that of the "nomad"...for the "nomad" cannot by the sheer definition form an alternate to what DeLeuze and Guattari call "the war machine": the manner in which a society exerts control (and the "war machine" itself is much more effective if coercion can exist without war). These horizontal connections among those who have learned to become organs without bodies, that is, banished the internal hierarchies within their own personal thinking and concept of organization of their own bodies, are a potential counteractive force against coercion...
OK. Beyond that, a few words. The book has chapters, called plateaus, but I'd have to say that there doesn't seem to be any great degree of organization. Indeed, DeLeuze and Guattari indicate that one could read the book in any order, skip large parts, etc. The most pivotal chapters are probably the first (simply to become acclimated to the writing, which is somewhat inscrutable, exhortational, and didactic all at the same time...truly remarkable, though it wears a bit thin after 400 pages of it), then "How to Become a Body Without Organs," then "Nomadology: The War Machine." Under no circumstances (in my opinion) should the chapter on "Nomadology" be read before the "body without organs" chapter; best flow is reading the ones that focus on the individual reaction to the linguistic implements of imperialism, then the ones that deal more with group reactions.
Anyone who is expecting some sort of detailed critique of capitalism (and, if you're reading this to begin with, you're probably not...ie, you probably know what you're in for, or are familiar with DeLeuze and Guattari, who are brilliant if a bit discursive), this isn't the book.
Finally, the book does reward patience, but (if philosophy is not your primary interest in your reading) you will need it...it is not an easy read, and the "plateaus" often "ramble" for 10-15 pages before they get to their core insight. Remember that, at their core, and amidst all of their other intellectual interests, what you have here is a philosopher/linguist and a psychiatrist who collaborated; in the end, everything is somewhat seen through the filter of language and how the use of language and other types of communication could possibly bring about changes of a society at its margins (while their posturing may suggest otherwise, I'd posit the idea that DeLeuze and Guattari are savvy enough to realize that most people aren't going to be able to read this book and understand it well enough to translate the concepts into potential society-changing thoughts on a large scale...).
But, if you really love DeLeuze, this is of course indispensable...though you'll probably already have read it. :)