What is Mildred's role in Fahrenheit 451?
Mildred's role is to showcase the vapid, pointless existence of the typical citizen in Fahrenheit 451. Her obsession with television and need to be just like everyone else -- to "fit in" -- causes her to become little more than an outlet for the opinions of other people. She is so disconnected from her own life that she refers to the cast of her favorite television show as "relatives" and "family."
He looked with dismay at the floor. "We burned an old woman with her books."
"It's a good thing the rug's washable." She fetched a mop and worked on it. "I went to Helen's last night."
"Couldn't you get the shows in your own parlour?"
"Sure, but it's nice visiting."
(Bradbury, Fahrenheit 451, Google Books)
Her mind is so filled with disconnected feelings and emotions that she has no response at all to his news that he killed a woman while working. It hasn't happened on her screens, and so it may as well have not happened at all. Even the television programs are not composed of story events, but of meaningless dialogue and sound effects. As he progresses in his development, Montag realizes how pointless his relationship with Mildred actually is.