The white clowns are part of a TV show. They are cartoon characters who do silly and violent things to one another, such as chop off one anothers' limbs. The show is filled with one violent act after another with tracks of canned laughter to accompany much of it. The purpose of this show and the clowns is to show the mindlessness of television and of the people in the society. The show also demonstrates the violence of the people and how little they care for one another. When Bradbury wrote the book, TV was still in its youth. Many people saw it as mindless entertainment that had the potential of robbing viewers of thought. The white clown exemplify this idea. Millie and most of the people in the society were absorbed by the antics of these cartoon characters. The viewers did not do any thinking as they watched this program. Also, Bradbury shows this society to be a violent one. When Clarisse talks with Montag in the first section of the book, she describes how many of her classmates have died in the last year in violent ways. We see people drive cars in reckless ways in the story and we also see how little feeling there is for one's fellow man. Again, the white clowns exemplify this violence and lack of feeling.
In Fahrenheit 451, the White Clown is a character from a show that is broadcast on the parlour walls. It appears in Part Two when Mildred arranges to watch it with her friends, Mrs. Bowles and Mrs. Phelps.
Like the parlour walls in general, the White Clown acts as a distraction from the realities of life. This is shown clearly when Montag asks Mildred if the White Clown loves her. Her reaction is to dismiss him; she doesn't want to think about such a deep question and prefers to live in the moment rather than ponder the bigger issues.
Moreover, the White Clown shows just how desensitized women like Mildred have become. When the White Clown show begins, for example, three white clowns "chop off" each others' limbs while laughter plays in the background. The women appear excited by the show and do not recoil at the scenes of mutilation. This reinforces the idea that they are so absorbed in entertainment that they have become ignorant to what is really going on around them.