A little knowledge is more successful than complete knowledge: it conceives things as simpler than they are, thus resulting in opinions that are more comprehensible and persuasive. (578)
Let us put aside the question whether anyone can have complete knowledge of anything, for what Nietzsche says won't be affected much if "complete knowledge" is replaced with "adequate knowledge" or "sufficient knowledge". First of all, note the "it" in "it conceives things as simpler than they are", which refers to "a little knowledge" rather than to the knowing agent. This sounds strange, because "a little knowledge" does not have a mind and cannot think. The German original is "es kennt die Dinge einfacher, als sie sind", and the literal translation of "es kennt" should be "it knows". Of course "it knows" does not sound any less strange than "it conceives", but I think what the whole expression means is "this is knowledge of things as simpler than they are". The "it" in "it conceives" or "it knows" is a dummy pronoun.
So, a little knowledge is knowledge of things as simpler than they are. Or more precisely, a little knowledge of X is knowledge of X as simpler than X really is. But why does "a little" imply "simpler"? This is because what is involved is knowledge of X rather than knowledge of part of X. If one's knowledge of X is little in the sense of being knowledge of merely part of X, then it is not necessarily simpler --- one's knowledge of part of X can be as complex as it (i.e. the part) really is, while the knowledge is still little compared to knowledge of the whole X. However, if it is knowledge of the whole X, it cannot be both little but not simpler.
A little knowledge results in "opinions that are more comprehensible and persuasive". Here the opinions are obviously opinions of the knowing agent --- the opinions are more comprehensible and persuasive to the knowing agent. But why are the opinions more comprehensible and persuasive to him? Well, because they are based on knowledge of things as simpler than they are. It is the simplification that makes the opinions comprehensible and persuasive. If the agent sees things as they really are, the complexity involved will perplex and humble him.
Nietzsche says "[a] little knowledge is more successful than complete knowledge. Successful in what sense? I can only think of one answer: successful in the sense of being treated as knowledge. The more one knows, the more one is not sure that one knows.