We generally think of wisdom and knowledge as good things, right? In The Turn of the Screw, it's hard to pin knowledge down as good or bad; the best you can really do is say that knowledge is fine…for some people. Even though our main character is a teacher, she seems to spend most of her time hoping that her children don't know certain things. We get the feeling that too much knowledge too soon is dangerous, and that some people go through their whole lives poorly equipped to handle the scary truths of the world. There's even the implication that knowing too much can lead to madness – or even to death.
The Governess's self-imposed role as a "screen" between the children and the ghosts allows her to accrue more knowledge than anyone else in the story, which in turn corrupts her to the greatest degree.
It is Miles's admission of his knowledge that ultimately kills him in the end; by dissecting the final chapter, we can see that relinquishing his secrets to the Governess also means relinquishing his life.