Human thought is immensely capable and also immensely error prone. Much of the task of philosophy has been dedicated to rooting out these errors. No philosophy has perhaps been more misunderstood and mystified, more prone to error, in this pursuit than that of Friedrich Nietzsche. Nietzsche's primary project can be viewed as the uprooting of a single pernicious error and the tracing of the consequences of its correction. This error is most easily summarized as the preference for being over becoming. By nature this correction accuses any preference for relations of equalization or "zero sum" equilibrium of committing a fundamental, all-too human error. Let's unpack these ideas further so we can clarify.
A vast array of Western metaphysicians have accepted the reduction of reality to what is - to being. This view of reality is, however, immediately troubled when the need arises to explain the passage of the present moment. If reality is being then why is this being constantly changing? To resolve this problem, what one might call the problem of genesis, the idea of negation and contradiction between co-existing beings has typically been taken up as the motor of passage. That gun turret over there is, until the missile explodes, then it is not. It has been negated or contradicted by the missile. If we could examine the missile itself we should find it explodes as a consequence of the resolving of its own internal contradictions. This is the Hegelian dialectic briefly summarized, from which one can derive all of first-order logic and mechanical physics, and for Nietzsche it is highly suspect for a variety of reasons. Suffice it to say that the idea of being confuses what comes last (what is) with what comes first (becoming). It thereby opens the door for all sorts of erroneous teleological principles (God, The Big Bang, The Big Freeze) to enter.
Nietzsche would like to substitute the notion of becoming in the place of being. He recognizes Spinoza as perhaps the only other philosopher to systematically approach this problem. We must ask along with Nietzsche, if being and negation cannot explain reality then what can we substitute in its place? The short answer is difference and repetition or becoming and eternal return to use Nietzsche's own vocabulary. Difference is the substance of reality, repetition is its motor. How are we to understand this?
Firstly, we will address difference. The fundamental nature of reality is difference. Every speck in the universe down to the subatomic particles and, perhaps, below is different from every other. Any being (identity) we find there is imposed after the fact by an abstraction from the particulars (representation). Thus the nature of reality is difference, but how does difference reconfigure itself? How does it solve the problem of genesis or passage?
The answer is, of course, by repetition. Everything recurs. Differences are ultimately relations of dominant and dominated between forces of various magnitudes. They are differential relationships. Each force, however, is driven to conquer those forces that dominate it and to dominate other forces. Think force in the same sense that electromagnetism and gravity are forces. Or, more mechanistically, this very inequality drives the evolution of new differences in a game without beginning or end. To get a concrete sense for this we have only to observe the differences in intensive quantities in physical systems (temperature differences, pressure differences, electrical potential differences). These differences power all the physical systems we know of. This is, very visibly, the game of dominant and dominated forces cyclcing endlessly around us.
This project Deleuze identifies in Nietzsche he carefully attempts to carry out in Difference and Repetition. To replace the erroneous "image of thought" associated with being with the "thought without image" associated with becoming. The transformation of the image of thought, on a personal and societal level, is extremely difficult. Thinking in terms of difference and repetition uproots the forms of the thought dominant throughout the Western tradition. It therefore leaves no easily accessible historical basis on which to constitute itself. Humanity is left with two options - lazily circling in the comfortable but erroneous form of traditional thought, or embracing the immense unknown of an entirely new form of thinking.
More and more our species is being forced by circumstance to embrace this Nietzschean way of thinking, though it may never, ultimately, be attributed to him. This vertiginous change is producing large-scale resistance and confusion in populations everywhere. To make sense of it requires tremendous fortitude in thought, and continual effort not to succumb to the allure of traditional thinking. Possible next directions for one interested in these new forms of thought: