In the context of the story, ignorance is defined as...
...lack of knowledge, learning, information...being uniformed; unaware...
Joyce Carol Oates' short story, "Where Are You Going, Where Have You Been?" centers around a character who is ignorant: Connie, fifteen-years-old, is belligerent with her mother, sneaky, and preoccupied with herself—especially with being pretty...and attractive to boys. Typical perhaps of a girl her age, Connie doesn't think her mother is especially intelligent:
Her mother was so simple, Connie thought, that it was maybe cruel to fool her so much.
The saddest aspect of this attitude is that Connie is the fool. Her mother worries about her for good reason. Her mother knows that the world is an unsafe place and she wants to protect her daughter. They may fight, but her mother is a knowledgeable woman with a desire to protect her daughter. She has not always been older and unattractive, but Connie is uninformed enough to believe her mother intentionally torments her, or to think that at fifteen, she can more easily navigate the world than her mother.
Connie is unaware when she goes off secretly to the drive-in diner across the highway that crossing a busy road might not be her mother's only concern if she knew. And Arnold Friend is a mother's worst nightmare: the kind of person she prays does not come to her town. Connie's lack of knowledge and information leaves her at a distinct disadvantage when Friend singles her out for his attention. He is a man of disguises, not only in terms of how he dresses, but also in how he acts. She doesn't have a chance.
Connie values beauty: Arnold looks good in his tight jeans and dirty shirt. She assumes he is her age. He seems like he may be a jerk, but does not come across as a threat...at first. Connie's first reaction is not of fear, but worrying about how she looks, for appearance is everything to her—an especially foolish notion...she runs about the house when the car arrives...
...wondering how bad she looked.
With a little more experience, Connie might have been worried with his first lie: that he is her age. And then he changes his story again to say he's eighteen—a lie. He's been caught in two acts of deception, but Connie isn't experienced or educated enough to see this as a threat. She is only slightly uncomfortable that he shows up at her house when she is alone. And instead of closing and locking the door, she engages in conversation with Friend that is at first flirtatious, later becoming dangerous as he manipulates and frightens her into giving up and leaving with him, without a struggle.
Where Connie lacks knowledge, Friend knows a lot...especially how to use his charm to get a girl close enough to tighten a noose around her neck. Friend has done his research to find out who she is and where she lives. Then he waits for a day when her family is gone. No alarms, no sirens: Connie doesn't know enough to be remotely suspicious. Her mind is preoccupied with love songs and promises. She lives in a fairytale world that never includes a demon or malevolent villain. Connie knows nothing that her mother knows about life; she does not value learning or knowledge—only appearances; and, she cannot conceive of an evil such as Arnold Friend.
Her ignorance allows her to accept appearances as truth, and to free her from the necessity of ever confronting reality—until it's too late. And that is when she realizes what she never knew.