Hello! An allusion is usually a reference to a person, place, or thing with any cultural, political, historical, or literary significance.
In the quote above, there are two allusions to two biblical verses. I will address both below:
To everything there is a season. Yes. A time to break down, and a time to build up. Yes. A time to keep silence and a time to speak.
This quote is from Ecclesiastes Chapter 3, verse 3 and Chapter 3, verse 7. In the story, Granger (the leader of the literary outcasts) tells Montag that he, Montag, would be the book of Ecclesiastes if something happens to Harris, another man who has committed the biblical book to his memory. Granger's group of geniuses have memorized whole books of important works. Despite the breakdown of society, their individual efforts at remembering the great works of world literature represents the building up of what has been lost or broken. They may keep silent to themselves for the present, but the implication is that the group will speak when the time is right and that they will share what they know when it is time to rebuild their lost society.
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.
The above quote is from Revelations Chapter 22, verse 2. The implication is that the catastrophic destruction of civilized society will not stand. The prophecy points to a time of healing. The tree of life references the many pages of wisdom committed to human memory; paper is mainly made from woodpulp (hence, the tree of life allusion). Therefore, safely nestled in the minds of individuals, wisdom from the 'leaves of the tree' (in a book, a single sheet of paper is a leaf; each side of the leaf is a page) will heal the nations at some future point in time.
This basically means that the wisdom derived from many pages of important literature (whether from Tom Paine, Thomas Jefferson, Machiavelli, Lincoln, Gautama Buddha or the Bible) will heal or cure the ignorance and degradation of humanity in the future. Hope this helps!