This title's meaning is exposed on the very first page of the story; after hearing a ghoulish tale in which a child is menaced by some ghostly terror, a party guest suggests that the fact that the story's protagonist was a child is what gives a certain "turn of the screw" – that is, it tightens the dramatic tension.
"I quite agree – in regard to Griffin's ghost, or whatever it was – that its appearing first to the little boy, at so tender an age, adds a particular touch. But it's not the first occurrence of its charming kind that I know to have involved a child. If the child gives the effect another turn of the screw, what do you say to two children – ?"
"We say, of course," somebody exclaimed, "that they give two turns! Also that we want to hear about them." (Prologue.2)
James' story offers a second "turn" by introducing a horror story about two children instead of one. Double the creepy kiddos, double the fun (or something like that).
This is an oddly mechanical way of describing the construction of a horror story—that is, a story that cranks the audience's stress level way up—and it keeps one of James's primary concerns, the craft of writing, in the back of the reader's mind at all times. The title also takes on a second meaning as we near the end of the story; the protagonist uses the phrase to describe taking control of her mental and emotional capabilities in preparation for a challenge.