An important thing to keep in mind when reading Nietzsche is that most of the time he is trying to reveal things through insights.
The point of this particular quotation is to reveal the assumption at the base of many philosophies (in this case, most specifically positivism): that objective facts exist.
Positivism holds, roughly, that the phenomena we observe through our senses are physical in nature and that they actually happen in a material world. Thus positivists take these phenomena as objective fact and use it for their world-explanation, for example by making physical laws. Nietzsche's statement is that fundamentally, positivists are interpreting observed phenomena as physical (instead of non-physical, e.g. Berkeley), and real, when in fact they have no definite justification to do so. Thus, facts are really the subjective result of information: there is nothing necessarily "true" about them, other than how they fit into a particular interpretation.
Just as the interpretation of a book is up to the reader, so too is Nietzsche pointing out that the interpretation of our world is up to the person observing. Now, here he does not make any claim as to whether, as with a book, there is an "author" who intended a particular meaning that we are supposed to pick up on, and that this meaning is the "correct" interpretation, but holistically that idea would probably be repugnant to Nietzsche: he effectively rejects all teleology, metaphysics, and meaningful notion of truth, which leaves no room for there to be a "correct" interpretation of the world.
Ultimately what this means is that, to Nietzsche, it is much less important whether we "understand" how the world "works" (if that is even a meaningful thing to say), and much more important that we develop an interpretation that works for us. One of Nietzsche's primary themes is the advance of humanity into a stronger (intellectually, culturally, and maybe physically) race, and the proper interpretation of the world could aid in achieving this. In Nietzsche's terms (and this is straying from this quotation against positivism to a generalized summary of Nietzsche), this would be the interpretation that best frees us from life-rejecting restraints such as Good vs Evil and lets us become stronger by exercising our will to power and working toward the overman.