The quotation is from Revelations and is a prophecy about the New Jerusalem. It's clearly meant to be a gloss on the state of Montag's society, which has been destroyed by war. Like Granger's comment on the phoenix earlier in the chapter, and the hope that, at some point, mankind will finally grow out of its need to destroy itself, the reference to Revelation suggests that a new and better society will arise, based in part on the old knowledge from books that they have preserved.

It's also interesting that Montag struggles to remember this passage, and, once he has it in his mind, decides he will save it up for the talk that will happen later in the day. He feels "the slow simmer of words" as he remembers, and there is a sense that he feels the words will have a sustaining power for his companions. This gets at the nature of prophecy and the function of words to not only record past knowledge, but to articulate possible futures. Whereas Granger's image of the phoenix prioritizes learning from the past, Montag's memory of Revelations uses metaphor to describe what they hope to build when they finally reach the city at the end of their journey.

This quote at the very end of Fahrenheit 451 comes from the biblical book of Revelation. In it, the speaker has a vision of the New Jerusalem, the final paradise in which heaven and Earth come together and humankind is redeemed. Humans will walk in the light of truth, not in fear of the destructive light of fires.

This quote is significant because despite Montag's society having been destroyed in nuclear war, the novel ends on a note of hope. First, Montag has escaped to one side of the river, but on the other side, where the ruins of the city lie, there is also hope: as the Revelation quote states, "on either [my italics] side of the river was there a tree of life."

In the novel, the tree of life is a metaphor for the knowledge which lies in great books of the past, which the men by the river, including Montag, have begun to reclaim. By associating books with the New Jerusalem, Bradbury invests them with a spiritual power.

The men who have memorized the contents of books are full of hope that they can use books' wisdom to rebuild society according to a better, sounder model. These "leaves" of truth, a pun on the leaves of the book and the leaves of the tree of life, once banned, are what will bring healing and rebirth to the Earth.

What is the significance of the biblical allusion to the "tree of life" in Ray Bradbury's Fahrenheit 451?

And on either side of the river was there a tree of life, which bare twelve manner of fruits, and yielded her fruit every month; And the leaves of the tree were for the healing of the nations.

Yes, thought Montag, that's the one I'll save for noon. For noon...

When we reach the city.

In Ray Bradbury's Fahrenheit 451, there are many literary and biblical allusions. At the novel's end, after Montag has crossed the river, he listens as others like him discuss having memorized entire books. Montag tries to remember things he has memorized, and one of those is a line from the Bible, specifically Revelation 22:2.

First of all, "Revelation" speaks to a "revelation," when God will show himself and his will to his people. The book of Revelation is also referred to as apocalyptic literature. The association of the book's intent is to provide a description of the "end times" and the promise of life afterward, as predicted in its chapters.

...the genre is known as apocalyptic literature. Such literature is 'marked by distinctive literary features, particularly prediction of future events...

In the scriptural passage noted, there is mention of "the tree of life."

The tree of life may symbolize the future of mankind: the book people who have escaped to the other side of the river. The fruit may be symbolic of the knowledge these people possess, which will nourish a new society. The leaves are said to be specifically for the "healing of the nations." As devastating bombings have occurred where Montag lives, and in other cities across the country, we can assume that the only hope for civilization is that it be rebuilt: specifically, Revelation refers to "healing"—we can assume of the land, the society and its people—the verse refers to the nation, which would be all of these things.

Whereas Revelation speaks to "reaching the city," (the "holy city of God") or Heaven, in this story, it alludes to a new life—one very different from that which these people have left: the society they have witnessed being destroyed. There is also a sense of resurrection: Revelations refers to it in a spiritual sense, but Bradbury may refer to a resurrection of not only Montag, but also of mankind:

'When we reach the city', the last line of the book, contains a solid link between Montag’s destructive world and the Apocalypse of the Bible, thus his spiritual resurrection.

When Montag says he'll "save it" for when they reach the city, he means he will speak of it when they arrive at their destination: where they will begin to rebuild society based on the knowledge they all have gathered collectively. Montag is delivered from destruction, and Bradbury leaves the reader with "a tinge of long-term hopefulness."

Additional Sources:

http://hubpages.com/hub/Symbolism-in-Fahrenheit-451

http://en.wikipedia.org/wiki/Book_of_Revelation