The Taming of the Shrew is an elaborate meditation on the workings of the theater and performance. Also known as meta-theatricality, this kind of self-reflective behavior is pretty common in all of Shakespeare's works, even the sonnets. From the play's frame structure to its inside jokes, Shrew is chock full of representations and references to acting, directing, staging, and spectatorship. In such moments, Shakespeare draws our attention to the fact that we are spectators at a performance while also blurring the boundaries between the stage and the audience. The audience is constantly forced to recognize the "theatricality" of everyday life, including the relationship between social roles and traditional stage roles. Of course, Shakespeare also manages to get in a few jabs at critics of the theater. (Those pesky old 16th-century Puritans who thought theater-goers were at risk for moral contamination and physical illness.)
The Taming of the Shrew intentionally blurs the boundaries between audience members and stage actors during the play, a reminder to the audience that they are, in fact, watching an artistic performance.
Characters' participation in frequent public spectacles emphasizes the theatricality of everyday life.