Good question. There are a few possibilities here. One conflict is between what the majority wants the masses to believe (keeping them blind to the real issues of the day, like the looming war, the shallowness of their lives, the high suicide rates) and what some individuals (represented by Montag and Clarisse's family) believe. The society believes you if you just keep the masses entertained, they will feel like they are leading a fruitful existence. This seems to work for many, but - again referring to the high suicide rates referenced in the text - for the independent thinkers in the society, it obviously doesn't work for them, which is why there is a need for the firemen.
Another possibility, is in how Beatty views books and how Montag and Faber view them. Beatty believes books are worthless because they really don't solve your problems. In other words, they blind you from the real world. Faber sees the opposite view (as does Montag later) that books teach us more about the world around us even if they are fiction. There are eternal truths that can be passed from one civilization to another - or from one generation to another.