The dentrifice commercial's content itself is not significant; Bradbury isn't trying to send subliminal messages about toothpaste or anything. Rather, it is the noise of the commercial, the place it is playing, and its mere presence that is important. Montag is on the subway, trying to read. The book that he is trying to read-the book of Ecclesiastes, from the Bible-feels to him, at that moment, like the answer to all of his problems. Just recently, he has realized how unhappy he is, how unhappy Mildred is, and how dumbed-down and unfeeling his society is. He has watched an old woman, Mrs. Blake, choose to burn to death with her books rather than give them up. Her conviction moves him, and he realizes he doesn't have that conviction in his life. So, he turns to books, and senses that they somehow hold the answer. So, he is desperate to read this book, and for it to speak to him.
However, as he is on the subway, the dentrifice commercial keeps playing, loudly, and ruining his concentration. He can't focus; he can't read. It is infuriating. This commercial is preventing him from having any rational, logical, followed-through thoughts. He realizes that the commercial is just one small part of a large whole in his society. Everywhere he goes there are commercials, keeping people from thinking. There is entertainment, diversion, deflection, and emptiness, all keeping him from thinking and feeling. The commercial, playing while he is trying to find answers to life through a book, just confirms what he had started to suspect: that the world he lives in makes it impossible to find happiness.
So, at this realization, he decides to go find Faber. He wants real answers, that can't be interrupted by society and its noise and commercials. The commercial pushes Montag over the edge, into full searching, into full realization of his society's subtle brain-numbing control over people. I hope that those thoughts help! Good luck!