Nietzsche does not fit any ordinary conception of the philosopher. He is not only remote from the world of the professorial or donnish philosopher, from tomes and articles, footnotes and jargon -- in brief, from the more modern image of the philosopher. He is equally far from the popular notion of the wise man: serene, past passion, temperate, and Apollonian. But this is clearly -- for those of you willing to explore -- part of Nietzsche's point: that is, to offer a new image, a philosopher who is not an Alexandrian academician, nor an Apollonian, but Dionysian.
Apollonian and Dionysian are terms used by Nietzsche in The Birth of Tragedy to designate the two central principles in Greek culture. The Apollonian, which corresponds to Schopenhauer's principium individuationis ("principle of individuation"), is the basis of all analytic distinctions. Everything that is part of the unique individuality of man or thing is Apollonian in character; all types of form or structure are Apollonian, since form serves to define or individualize that which is formed; thus, sculpture is the most Apollonian of the arts, since it relies entirely on form for its effect. Rational thought is also Apollonian since it is structured and makes distinctions.
The Dionysian, which corresponds roughly to Schopenhauer's conception of Will, is directly opposed to the Apollonian. Drunkenness and madness are Dionysian because they break down a man's individual character; all forms of enthusiasm and ecstasy are Dionysian, for in such states man gives up his individuality and submerges himself in a greater whole: music is the most Dionysian of the arts, since it appeals directly to man's instinctive, chaotic emotions and not to his formally reasoning mind.
Nietzsche believed that both forces were present in Greek tragedy, and that the true tragedy could only be produced by the tension between them. He used the names Apollonian and Dionysian for the two forces because Apollo, as the sun-god, represents light, clarity, and form, whereas Dionysus, as the wine-god, represents drunkenness and ecstasy.
Finally, a word or two from Walter Kaufmann:
Nietzsche's ideas about ethics are far less well known than some of his striking coinages: immoralist, overman, master morality, slave morality, beyond good and evil, will to power, revaluation of all values, and philosophizing with a hammer. These are indeed among his key conceptions, but they can be understood correctly only in context. This is true of philosophic terms generally: Plato's ideas or forms, Spinoza's God, Berkeley's ideas, Kant's intuition all do not mean what they would mean in a non-philosophic context; but scarcely anybody supposes that they do. In Nietzsche's case, however, this mistake is a commonplace -- surely because few other philosophers, if any, have equaled the brilliance and suggestiveness of his formulations. His phrases, once heard, are never forgotten; they stand up by themselves, without requiring the support of any context; and so they have come to live independently of their sire's intentions.
image caption: The Theater of Dionysus is said to be the place where Greek tragedy began.
[Source: Walter Kaufmann, From Shakespeare to Existentialism: An Original Study (Princeton: Princeton University Press, 1959), pp. 207-8.]