Dogmatism, to Nietzsche, is taking any claim as an absolute truth that does not need to be justified. While philosophers claim to base everything in reason and to take nothing on faith, Nietzsche argues ultimately that all philosophy is grounded on some leap of faith. It is logically impossible to create a system where every claim in the system is justified by another part of the system. If we see a system as a building, where every block has to rest upon another block, we ultimately must arrive at the foundation blocks upon which all the other blocks rest. Philosophers generally take the foundations of their systems to be very simple and indubitable truths. Nietzsche, on the other hand, takes these foundations to be childish superstitions and prejudices. Nietzsche operates on the maxim that a claim taken as obviously true is really just based in assumptions so deep that we no longer recognize them as assumptions.
Nietzsche is often difficult to understand because he argues against anything that parades itself as an absolute truth, and our thinking is so influenced by a belief in absolutes that it is often difficult to take Nietzsche at face value. His position, which has been called "perspectivism," insists that there are not absolute truths, but only different and equally valid perspectives with which we can look at the truth. We might think of truth as of a sculpture: by looking at it from only one side, we don't understand or appreciate the whole sculpture. Only by walking around it and looking at it from all different angles can we properly appreciate it.
Nietzsche's main objection to Platonism is that it fixes our perspective, saying "there is only one truth and it must be looked at in this way." Such an insistence paralyzes our understanding and makes it impossible for us to reason freely. Nietzsche's ideal of "free spirits" is of people who do not allow themselves to be tied down to any one perspective, dogmatism, or faith.
The themes outlined in this preface serve to introduce the frame of mind with which the rest of the book must be approached. Nietzsche is essentially saying: "check all your assumptions at the door. I will not accept any objections that are based on any kind of dogmatism."