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.