The Turn of the Screw is written in an incredibly dense, winding, and circuitous literary style. For contemporary readers, the prose might feel frustratingly impenetrable at times, as James often uses double negatives and writes complex sentences with many dependent clauses that make it hard to track his use of nouns and pronouns—that is, it can be hard to follow what's happening!
For example, take this progression of sentences from the final scene, in which the governess is trying to get Miles to tell her why he was expelled from school. As she's questioning him, she turns and sees the ghost of Peter Quint staring through the window:
I felt a sick swim at the drop of my victory and all the return of my battle, so that the wildness of my veritable leap only served as a great betrayal. I saw him, from the midst of my act, meet it with a divination, and on the perception that even now he only guessed, and that the window was still to his own eyes free, I let the impulse flame up to convert the climax of his dismay into the very proof of his liberation.
If these two sentences seem quite layered and hard to follow, it's because they are. This circuitous style is especially noteworthy here because this is a significant moment in the narrative—the moment just before Miles dies of some sort of shock. The dense and ambiguous language obscures what's happening, and this contributes to the unsettling effect of the entire tale. The tangled sentences add to the prevailing sense of uncertainty in the novella.
Finally, it's worth noting that some critics partially attribute Henry James's increasingly dense prose to the fact that he switched from writing his own work to dictating it—a switch he made just a year or so before writing The Turn of the Screw.