A euphemism is a nice way of referring to something "unpleasant or offensive." For instance, someone might report that a person passed on rather than saying he or she died. "Powder room" used to be a nicer way of referring to the bathroom.
In Ray Bradbury's Fahrenheit 451, one euphemism might be when Beatty refers to a man whose house they had burned:
They took him screaming off to the asylum.
In the next line, Montag clarifies by saying the man wasn't "crazy." Beatty's description is slightly more positive than using the word insane. When the firemen go to 11 No. Elm to burn the house, with its owner still inside, she quotes Hugh Latimer, a Protestant clergyman in England who tried to comfort a friend, both of whom were going to be burned at the stake as heretics (during the reign of Mary I or "Bloody Mary"). Latimer (using a metaphor) says "we shall this day light such a candle...", which actually means that their deaths will serve to pave the way to change. It is certainly more pleasant than stating that they shall be burned alive.
If a euphemism is a nice way to refer to something unpleasant, we might look to Bradbury's description of Beatty at 11 No. Elm.
...his pink face burnt and shiny from a thousand fires and night excitements.
Burning the homes of book owners hardly seems as harmless as the term "night excitements" would lead the reader to believe. These experiences are horrific, and once the woman at 11 No. Elm takes her life (a euphemism for suicide) rather than to be separated from her books, Montag can no longer continue working as a fireman. He not only finds no pleasure in it—he conscience cannot allow him to participate in burning one more house.