Joyce Carol Oates' is the author of the short story "Where Are You Going, Where Have You Been?" It was based on a true story of a serial killer in the 1960s in Arizona; the antagonist, Arnold Friend, is fashioned after this "insecure and charismatic" murderer.
The significance behind the word "glance" is that it only provides a brief and superficial perception of something because it is done quickly, without complete attention to what is being "seen." It is with a glance that Connie first sees Arnold Friend, but as "glance" indicates, she doesn't really see him until it is much too late.
She drew her shoulders up and sucked in her breath with the pure pleasure of being alive, and just at that moment she happened to glance at a face just a few feet from hers.
This line contains—in essence—Connie's birth into adulthood (she believes), and her death (making casual eye contact with the man who will take her life). In the context of the story, it is a powerful word. What she thinks she sees in this glance is a "boy with shaggy dark hair." However, when he shows up at her home, she realizes too slowly that he is not as he first appears. She doesn't know enough to take a second, closer look.
In that first glance, Friend is driving a convertible jalopy painted gold. When he shows up after her family has left the house, the car seems terribly bright, but at second "glance," it has been recently painted, is dented, and has crazy writing in different places.
Unfortunately, when Connie "happened to glance" at Friend the first time, "she couldn't help glancing back..." and this, it would seem, seals her fate.
...there he was still watching her. He wagged a finger and laughed and said, "Gonna get you, baby..."
Her glance does not take in enough information. Looking closely at him outside of her home, she notices his hair—like a disguise...
...shabby black hair that looked crazy as a wig...
She thinks he is her age, but realizes he is almost thirty...and he lies about it, but still the wrongness of the man doesn't register. At first, his eyes are hidden, but when he does take off the sunglasses, his eyes are frightening. Again, her glance does not take it in:
...she saw how pale the skin around his eyes was, like holes that were not in shadow but instead in light. His eyes were like chips of broken glass that catch the light...
His eyes are like holes—the author does not say that they reflect the light, but compares them to holes, and includes "shadows" in conjunction with them. Though they look like glass, the glass is "broken." Arnold is broken, too.
The casual glance makes Connie think that he is like the rest of the boys her age. He wears clothes like other boys, but on Friend, the clothes hide the real man. His boots are filled with something, perhaps newspaper, to make him appear taller. Connie notices, too, that his face is like a mask...she sees what he wants her to see. She even misses his frightening behavior because she never takes a really good look:
...the nose long and hawklike, sniffing as if she were a treat he was going to goggle up...
The sense of a predator comes to her much too late. What she thinks she sees is only an illusion Friend has created, using her inexperience against her so she allows him close enough to work his way into her brain, threaten her family and rob her of hope.
In the end, she is betrayed by a glance, and goes with Arnold Friend without even a whimper.