The Governess is the only character we can really sink our teeth into in this story—in fact, maybe we should just go ahead and say that she's the only real character.
Everyone else is a bit ghostly (pun very much intended) but the Governess is a flawed human. And we mean flawed-flawed—we're never quite sure how trustworthy she is as a narrator.
But, hey: she keeps us on our toes.
As for the facts, they are relatively few and far between: we know that she's only twenty years old, and that she's the daughter of a poor country parson. She's clearly something of a romantic, at least at the beginning, and this inclination contributes to her acceptance of the job at Bly. Though she only meets her employer twice, she's sufficiently swept off her feet, and spends the rest of the story secretly in love (or lust) with him.
Now that we've got the easy stuff out of the way, it's time to tackle the more complicated elements of the Governess's personality. There are traditionally two ways of viewing her character—as either a sane heroine or a insane anti-heroine. Both sides have passionate adherents; if you ever want to pick a nasty fight in a room full of English majors, bring up The Turn of the Screw.
Let's take a look at both of these cases—we leave the final verdict up to all of you.
The classic reading of this story is that we assume that our heroine to be in full possession of her mental faculties (that is, she's not crazy), and that all of these supernatural things actually take place in the real world.
This view of the Governess places her in the role of the traditional heroine, and assumes that she is really acting for the good of the children; it also assumes that the children are in fact in cahoots with the ghostly visitors, and that both Flora and Miles are little deceivers.
And there's some textual evidence to support this, honestly. Check out the way she speaks about Miles shortly after meeting him:
He had never for a second suffered. I took this as a direct disproof of his having really been chastised. If he had been wicked he would have "caught" it, and I should have caught it by the rebound – I should have found the trace. I found nothing at all, and he was therefore an angel. (4.4)
When the Governess first meets Miles, she's anticipating that she'll see some sort of residual "wickedness" in him—that there would be something that suggested he did something worthy of being kicked out of school. But, when she looks for this, she sees only a boy who's angelic almost to the point of being otherworldly. This hints at Milo's deception rather than her lack of judgement, honestly.
So: if we're to look at things this way, then we see the Governess as a strong-willed, intelligent, and noble young woman, who ultimately ends up a victim of Quint and Jessel... and being duped by a couple of little kids.
The most popular alternate reading of the character is that the Governess is 100% certifiably insane, and that the supernatural activity is all a manifestation of her tormented, repressed mental state.
This psychoanalytic perspective was first proposed by the influential literary critic Edmund Wilson, in a 1938 essay entitled "The Ambiguity of Henry James." In the essay, Wilson carefully lays out several instances in which he sees signs of Freudian symbolism in the story; the Governess stands out as a neurotic, sexually repressed woman, whose hidden desires drive her mad.
Just check out this passage to see a little bit of what Wilson's talking about:
It was a pleasure at these moments to feel myself tranquil and justified; doubtless, perhaps, also to reflect that by my discretion, my quiet good sense and general high propriety, I was giving pleasure – if he ever thought of it! – to the person to whose pressure I had responded. What I was doing was what he had earnestly hoped and directly asked of me, and that I could, after all, do it proved even a greater joy than I had expected. I daresay I fancied myself, in short, a remarkable young woman and took comfort in the faith that this would more publicly appear. (3.9)
The choice of words in this paragraph are pretty saucy. It's impossible to read a sentence like "I was giving pleasure [...] to the person to whose pressure I had responded" and think "Oh, well that's 100% innocent with no possible sexy overtones."
We know that the Governess thinks the uncle is a hottie with a body—we just don't know whether this crush is driving her insane.
So we'll leave it up to you: has the Governess lost her marbles thanks to a combination of isolation and libido? Or is she just a woman who's justifiably freaked out by living in a manor that a couple of ghosts are using as a crash pad?