This quote comes at the first climax, when Montag faces Beatty. Beatty is forcing Montag to burn his own house and all the books he has stolen, and then Montag will be arrested and probably executed. Montag, still in the passionate grip of his new-found individualism, is resisting; Beatty, a master of language and words, is trying to convince Montag one last time that the future society's philosophies are correct:
"What is fire? It's a mystery. Scientists give us gobbledegook about friction and molecules. But they don't really know. Its real beauty is that it destroys responsibility and consequences. A problem gets too burdensome, then into the furnace with it. Now, Montag, you're a burden."
(Bradbury, Fahrenheit 451, Google Books)
Beatty is explaining that this philosophy is all about the immediate, the present time, without concern for the past or future. Anything that doesn't fit in with the present is a burden, and must be destroyed; historically, fire is the ultimate destroyer, cleaning the surface for the next event. After the fire, who is to know what was said, or done, and when, and for what reason? Beatty wants the books destroyed because it absolves him and everyone else in the society from their responsibilities as humanity; they can ignore everything except what happens on their television screens, and trust the fire of the firemen to keep all other influences at bay.