Ray Bradbury tells us that 451 degrees Fahrenheit is the temperature at which paper burns.
As far as the importance of the fireman's job, it is to keep people happy. Bradbury tells us that books made people think too much. When people would think too much, they would become unhappy. So the society started to have the elaborate television systems (the parlor walls) and violence and fast cars and such so that they could not have to think.
The fireman's role in this is to make sure that no books can survive to threaten this ignorance.
Bradbury has brought back into play the role of the fireman from a previous book he had written. The fireman is the book burner. The books could represent enlightenment which can not be available to the people. The burning of books represents the erasing of the mind. The firemen assist in erasing wisdom from the people which helps to control them. The result is a dystopia where the people lack imagery and imagination. The fire men also go to people’s homes to retrieve the books for burning. The significance of the number 451 is that at 451 degrees Fahrenheit paper will burn; hence the paper of the books; the words penned on paper.