The characters, Mildred and Montag are referring to a script that Mildred regularly orders. In the society that they live in, television programs specifically tailor their scripts so that their viewers can participate with the characters on the parlor walls. Mildred refers to her part in the script.
Montag notices how in these scripts, there is really never much content to what is said. It is strange to him, and by extension the reader, how consumers of these television programs order scripts so they can practice having relationships with characters when they could just engage in relationships with the people in real life.
These scripts are an important part of the novel because they reveal yet another feature of the loss of humanity in the novel's society.