I assume that when you say "the 'M' word," you mean "magic."
Uncle Vernon and Aunt Petunia are very strongly against the use of magic and even against its existence. They are both ashamed of the idea that one of their relatives is a wizard. By the time this story happens, the only reason Rowling gives us for this is that they are too much of Muggles -- that they are too stubborn and unimaginative.
Later on (Book 6) we find out that Petunia had wanted very badly to be magical herself once she found out Lily was magical. So some of her problem is jealousy.
Actually both petunia and vernon were really SCARED of magic although they show of that they hate this word only....moreover as they were really asahmed that lily was a magicain they want to hide that thing and t0 save their beloved son DUDLEY from this stupid thing.....