With this context in mind, "edge" in relation to content seems to refer to the distinctive features of a particular text that separate it from all other texts of similar genre and define it as belonging to a certain group or audience. Edge is the content that it is tailored to provoke identification or emotion in an audience - and it can be "edgy" because it won't provoke the same feelings from every person that comes across it, especially if the text is consumed across the boundaries of the producer's perceived audience groups. On page 197, Curtin discusses the culture industry's goal of "striving for broad exposure through multiple circuits of information and expression." These individual circuits are the unique and creative edge added to particular shows in order to "establish clear taste boundaries" that Havens and Lotz speak of.
Throughout this article, I thought of the Twilight series books and movies as an example of a media text that can be considered "edgy" by this definition. It has more than a clear target audience - every text must at least have that. However, this story line has a more unique identifying trait in a strong female protagonist who is meshed with a popular fantasy love story. These books were a gateway to an entire genre of vampire fiction, proving that an audience did in fact exist to consume this type of media. In the context of media production, Twilight certainly has an "edge," in that it discovered new boundaries of audience demographics and played on those to create both an immensely popular text and genre.