I assume that you are talking about the part where Montag is on the subway, headed for Faber's house. He is trying to read the Bible but the Denham's ad keeps preventing him from concentrating.
The part of the Bible that he is reading is the Sermon on the Mount. This is from the Gospel of Matthew, Chapter 6. Specifically, he is reading the part where Jesus talks about how flowers get all they need without working for it -- through God's grace.
I think this applies to Montag because of a couple of things:
- He needs help and this is saying God gives help.
- He needs to feel that it is okay to relax. His society says relaxing is bad, but this passage tells you it is okay to relax because God will take care of you.
In Fahrenheit 451, Montag is trying to memorize the words Jesus spoke concerning lilies:
Consider the lilies of the field, shut up, shut up.
But he keeps getting interrupted by a commercial blaring through the subway.
First, the book he is reading, the Bible, is important simply because it is a book in a bookless society, and it relates to Montag because he is openly reading it in public. This is a big step for Montag.
Yet, he can't understand what he reads. This leads him to think of the sieve and the sand anecdote and image and metaphor, as he compares the futility of trying to fill a sieve with sand, with his attempt to comprehend and remember everything he reads.
Specifically, his memorizing of the lilies of the field passage reminds one of Clarisse's desire and ability to notice nature, to experience nature. This is a central part of her influence over Montag. A lilly, perhaps, might also be reminiscent of the dandelion she rubs under his chin, establishing, or at least suggesting, that he is not in love.
Finally, Montag's attempt to memorize a text in order to save it, is an important step toward saving a part of existence that makes one human: knowledge, opinions, ideas--all contained in books.