Nihilism is the belief system of nothingness. Nietzsche did not want a nihilistic world. He warned us against it. Nihilists believe that all "power" (think noble power, as in noble romans or noble greeks) should be dissipated. Nietzsche called it slave morality because the weak majority fettered the strong noble majority. Nietzsche, more than any philosopher since Plato, has shaped modern culture. He influenced Derrida and Foucault. Both who have proven that everything is relative to perspective.
For example: Someone mentioned ealier that sex is the basis for life. Foucault in his book "The History of Sexuality" shows us that sexuality has meant myriad things over time. That there has been a huge discourse on sexuality that has changed the connotation of it immeansely. Now-a-days we have a sex-life. We can discuss our sexlife amongst each other. In, say, the 1500s if you asked someone about their sexlife (or connotational equivilant) they'd look at you like you were crazy. To them a 'sexlife' was no different than a 'sleep life.' Sex was something as natural as sleep, or eating or whatever.
Nietzsche did the same thing for morality. In his book "Genealogy of Morals" he traces western concepts of "Good" and "Bad" to their pre-christian roots.
Saussure wrote an essay on the fact that all language is relative. That no language has any a priori essence. That if we call something a tree, the sound "tree" is relative to the word "tree" which is relative to the object of a "tree."
Derrida used this to show that despite the entirety of abitraryness, we still have to impose some sort of quasi-metaphysics because of the connotation associated with every word.
If anyone cares I'll explain in more detail, but hopefully this explains a little
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