The word "movie" in this powerful short story is important because it is part of the deception that Connie uses to trick her parents and convince them that she is merely going to watch a movie with some girlfriends, whereas in reality she is going over to a drive-in restaurant to interact with boys. The parents are tricked by Connie and so she is able to grow up very rapidly free from the scrutiny of her parents. This two-sided element of Connie's character is integral to her development:
Everything about her had two sides to it, one for home and one for anywhere that was not home: her walk, which could be childlike and bobbing, or languid enough to make anyone think she was hearing music in her head...
The "movies" that she apparently goes to see are just another sign of this two-sided nature. To her parents, they represent her childlike, innocent nature as she goes to see them with her girlfriends. In reality, however, when she goes to see "movies," she is entering the uncensored world of adult relationships.