In a world where individuality is nonexistent, all are expected to think and behave the same; even the words to denote individuality or references to the first person are nonexistent. Even to discover or utter the word "I" is punishable by death; it is only referred to in the work as the "Unspeakable Word." Equality relates his experience when he was 10 and watched The Saint of the Pyre burned at the stake for some crime; he deduces that the Saint was attempting to communicate the concept of individuality, expressed in the word "I" to him.
Quite simply, in the book, Anthem, written by Ayn Rand, the Saint of the Pyre is trying to communicate the banned word "I." Of course, uttering the word "I" is punishable by imminent death in the book, so the Saint of the Pyre has to convey the word "I" in another way.
The way the Saint of the Pyre chooses to explain the word "I" to Equality is by explaining the concept of individuality (as banned a concept as the actual word). Just think of the irony of that statement: explain individuality to a character named Equality!
Here is a quotation that gets right to the point:
I am done with the monster of "We," the word of serfdom, of plunder, of misery, falsehood and shame.
And now I see the face of god, and I raise this god over the earth, this god whom men have sought since men came into being, this god who will grant them joy and peace and pride.
This god, this one word:
Here we can see that we is, in fact, a "monster." It is a monster that takes all individuality away. We can see this in the description that follows of all negative attributes (even "shame"). How interesting to describe the "face of god" as the word "I." This idea is then followed (to juxtapose the first) by listing many positive attributes the "god" of "I" will "grant" such as happiness and peacefulness and even pride.
In the novel, Anthem, written by Ayn Rand, the usage of the word ‘I’ is banned and all the characters are expected to use ‘we’. Saint of the Pyre, however, tries to communicate the unspeakable word ‘I’ to Equality. In attempting to communicate the unspeakable word, the Saint tries to convey the concept of individuality to Equality.
The Saint chooses to impart the knowledge of individuality to Equality because he sees qualities of himself in Equality that remind him of the spirit of independence and braveness he also possessed.
Therefore, the flashback to the burning of the Saint is a symbolic torch-passing from a dying hero to a young man who will continue the fight for individualism in their society.
The Saint of Pyre was being punished for speaking the 'Unspeakable Word' which no one knew. While burning, it is most probable that the Saint of Pyre was looking at Equality, a child (children symbolise hope and future) to try to convey the message, of not just the Unspeakable Word, but of the idea of individualism.