There are three types of representative conversations: one that represents what type of society that people in Montag's society live in, one that represents how their society got to be that way, and one that describes the value of reading books and thinking.
The first representative conversation is had between Montag and Clarisse, in several different sessions as they run into each other as Montag comes home from work each day. Clarisse informs Montag that at school, the kids are crammed with information and not allowed to ask questions, that kids don't talk or connect anymore, but instead go out and do violent things, often killing each other as a result, and that her family is considered different because they actually like each other and spend time talking to one another. We learn that she is "antisocial" because she likes to question and think about things, and that there is no such thing as meditation, the arts, or finery anymore. These bits of information, coming from Clarisse, let us know right off the bat what their society is like.
Next, Beatty comes and tells Montag how they became that way. He informs him that it was a combination of mass media, trying to please large crowds without offending minorities, sheer laziness, political correctness, and government taking advantage of the situation. This helps the reader to understand how their society came to be so mindless and shallow, and helps us to recognize similarities to our own society today, and draw lessons from those comparisons.
The last representative conversation that is had is between Faber and Montag. Montag goes to him wanting to know why books are important. Faber indicates that it is because they quality and depth to them, they give you space and room and encouragement to think things through for your own self, and that they prompt action as you act on what you have learned. It is more what books help your brain to do--think independently, and to value life for what it is--than the actual paper and covers that is important.
These three conversations represent the themes and important messages that Bradbury wants to convey, that relate to the dangers of a brainwashed, mindless society as a result of over-entertaining and political correctness. I hope that these thoughts helped; good luck!