Deductive reasoning is the process os using previously accepted statements to draw a conclusion.
I'll show you an example.
A detective determines that <em>the person who committed the crime is a relative of the victim and walks with a limp. Since the mayor of the town is the only person who is a relative of the victim and walks with a limp</em>, the detective uses deductive reasoning to determine that the mayor of the town must have committed the crime.
The previously accepted statements are in italics and the conclusion is shown in bold.
The significance of this quote is Montag's realization of what his job is actually about and what it implies. He became a fireman because he was meant to. However, he is now haunted by this new feeling and does not know anymore what is right and what is wrong.