I assume the conversation you refer to is the one in Part 1 when Beatty comes to Montag's house after Montag fails to report to work following the burning of the old woman. The conversation indicates that Beatty knows Montag has books. Beatty says that all firemen, at one time, become curious about the books they burn, it's understandable and the authorities will overlook it as long as the fireman comes to his senses and gets rid of the book. The conversation is also meant to tell us, the reader, how the society of the story came to be. Beatty explains the progression of political correctness and a desire for condensed information coming at a high speed. He goes on to explain how focus was put on "fun" and taken off education, how society pushed for younger and younger children to be put in "schools". The alienation that is prevalent in the story's society can be traced back to all of this. Books were eventually banned because of policitcal correctness and because no one had time to read anyway - at least that's what Beatty says. What he is careful not to say is that the authorities knew that if they kept the populace amused, busy, and dumb that the populace would be easy to control.