The narrator of the story is not involved in the action, and we have no idea how he even got wind of Billy Budd's story in the first place. Yet in many ways, he is a realistic third person narrator. In a lot of 19th-century novels, the narrator tries to make himself invisible, but at the same time he's everywhere. He knows exactly what happened in great detail, and can even tell you what different people were thinking at any given time.
The narrator of Billy Budd is different. Regardless of how he learned the story of Billy Budd, he often admits that his knowledge of the situation is limited. The most glaring example is that he refuses to explain why John Claggart hates Billy Budd. He philosophizes and speculates, but he lets the two central characters – Claggart and Billy – remain a mystery to him and us. Another example is when Vere goes in to tell Billy that he will be executed. The narrator says that no one knows what happened, and again admits that he is just venturing some guesses. In these cases, he's admitting his subjectivity, but (and think about this for a moment) only to try to give us a more objective view of things. By admitting what he doesn't know, the idea is that we should have that much more faith in what he does tell us.
Notice, however, that the narrator is totally inconsistent. For example, how does he know what took place between Billy and the afterguardsman when the two were alone on the deck in the middle of the night? Furthermore, even if he admits that he is speculating, he is painting a picture of John Claggart and Billy Budd that becomes a part of the story he is telling. He takes the little kernel of truth – Claggart falsely accused Billy of mutiny and then Billy killed him – and works backwards. We have no way of knowing what else is truth and what is imagination. As he paints it, Claggart is simply evil and Billy is simply good. Is this a reliable way of viewing the two main characters? Unlikely.
Overall, the point is that you should pay very close attention to what this "Third Person Objective" narrator is telling you and not telling you because, when you get down to it, he's not really objective at all.