In Part One of Fahrenheit 451, when Montag and the other firemen are about to set fire to a woman's house, he comes across this line of poetry. This is an allusion to a collection of essays called Dreamthorp, which were written by the Scottish poet Alexander Smith.
At first glance, Montag is drawn to these words because of the soft and peaceful image they create. This contrasts sharply with Montag's current environment: he is surrounded by illegal books in the attic, waiting for the order to torch this house and its contents. As such, this poetry offers a brief, though welcome, escape.
On a deeper level, however, Montag is drawn to this line because, subconsciously, he is already beginning to question the fireman system and his society's widespread use of censorship. In this way, these words foreshadow the future events of the novel in which Montag comes to understand the beauty and importance of books and reading.
Prior to reading this line, we get a hint of Montag's (and the firemen's) thought process as they investigate a house. They feel that since the house, books, and objects are just "things," things without feelings, it is all right to bash and burn.
And since things really couldn't be hurt, since things felt nothing, and things don't scream or whimper, as this woman might begin to scream and cry out, there was nothing to tease your conscience later.
Books, like other objects that have no feelings, could then be burned without any thoughts of guilt. However, a book literally falls into Montag's hands "like a white pigeon, in his hands, wings fluttering." The book seems to come alive. And he reads the line and has some indication or intuition that this book has thoughts in it. So, although he previously burned books with reckless abandon, this was a subtle indication to him that there is something living, or at least some trace of living thoughts in books. It was not so much the line itself as the event as he experiences it and the fact that he's simply given a chance to read anything at all. He drops it and then steals the next book that falls. Just one poetic line was enough to entice him.
The line comes from Dreamthorp by Alexander Smith which is a collection of essays about the country.