Why did the old lady light the match and commit suicide in Fahrenheit 451?
The old lady decided to commit suicide because she was sending a message that books are too valuable to live without.
In Fahrenheit 451, people have decided that books are dangerous and we should live without them. They have purged their society of all books. Having books is a crime, and anyone who possesses them is a criminal.
At the time he arrives at Mrs. Blake’s house, Montag is beginning to have serious doubts about society’s treatment of books. He is already starting to be curious about them when he takes one from her house. When he sees her light a match, he is even more curious.
The woman on the porch reached out with contempt for them all, and struck the kitchen match against the railing. (Part II)
What could make books so important that a person couldn’t bear to live without them? Montag decides he needs to find out? That is why Mrs. Blake commits suicide. She is sending a message to Montag, Beatty, and the other firemen that their job is not protecting society as they think it is. By protecting the status quo, they are preventing people from experiencing their real humanity, as they only can through the collective wisdom of years of literature, philosophy and religion.
Montag doesn't understand why Mrs. Blake says, “Master Ridley” to him, and Beatty explains.
"`We shall this day light such a candle, by God's grace, in England, as I trust shall never be put out"' said Beatty. (Part III)
The old woman is aware that by lighting herself on fire, she is lighting a fire in Montag to share the value of books. He will be so consumed with wondering why she did it that he will need to look at the books himself, and it will lead him to question everything he believes in to the point of killing Beatty and going on the run to find the book people and save civilization.