The logic in Tolstoy’s beloved and inspirational story “What Men Live By” seems a bit convoluted at times but gets sorted out if the subtle shades of meaning are attended to. The three truths that the displaced angel learns answer the questions:
What dwells in man, What is not given to man, and What men live by.
The answers were revealed through daily living experiences in the shoemaker's cottage. One meaning of "significance" is the import or consequence of a thing. If this meaning is used, then the significance is that the truths released the angel Michael from his punishment and allowed him to return to heaven. His punishment to live like a mortal man was given because he allowed a dying mother to convince him that humans live by fulfilling the needs they perceive as she thought of her new born infant daughters. Living on earth with the shoemaker, Michael learned what humans truly live by, along with what dwells within humans and what is not known by humans.
I have been punished, but now God has pardoned me. And I smiled three times, because God sent me to learn three truths, and I have learnt them.
"Significance" also means simply meaning. By this definition, the meaning of the three truths learned by Michael are these. The first truth is that what "dwells in" humans is love. The shoemaker's wife was bound up in fear for the winter and adequately meeting their needs, then, when spoken to of God by her husband, she remembers the admonitions to love and help those who are suffering. In so remembering and doing, she showed Michael pity and that love dwells within. Later, the second truth was revealed when the man ordered boots to last a year, Michael could see by the presence of the angel of death that the man's life would go no longer than that night. From this he learned the truth that humans do not know their own needs; this is further significant because Tolstoy makes the point that humans are meant to live in unity instead of in solitude.
The significance of the third truth is that what humans live by is love. Love, then, has double significance: it is what dwells within and is shown as pity and kindness, and it is what humans live by as others meet our needs. The significance is compounded when the two are considered in relation to the second truth: humans don't know their own needs.
Tolstoy is emphasizing his philosophy that humans are meant to live in unity on a foundation of love that gives (as the shoemaker's wife gave) what is needed to humans who do not know what they need (such as the man did not know his needs for soft slippers) because what humans live by is love freely given (as the woman gave to the twin girls). Tolstoy creates a closed circle of life that both begins and ends with love: love is the motivating power within a person and love is the saving gift that is received by another person in a life in which one cannot know one's own true needs.
The orphans remained alive not because of their mother's care, but because there was love in the heart of a woman, a stranger to them, who pitied and loved them. And all men live not by the thought they spend on their own welfare, but because love exists in man.