What is Odysseus' epiphany regarding mortality through his visit to the land of living dead in book 11?
When Achilles comes forward to speak to Odysseus in the Underworld, Odysseus assures Achilles that he is awarded "'equal honor with the gods'" on earth because of how revered he is. Odysseus tells Achilles "do not grieve at having died [...]." However, Achilles is not comforted by Odysseus's words, and he says,
Mock not at death, glorious Odysseus. Better to be the hireling of a stranger, and serve a man of mean estate whose living is but small, than be the ruler over all these dead and gone.
In other words, Achilles says that any life—even one in which a person is poor and powerless—is better than death, even a death where one is honored and revered. There is no honor in death that makes up for the fact that one is no longer living. The only news that seems to bring Achilles any joy or peace is news of his son. He asks Odysseus to
[...] tell [him] tales of [his] proud son, whether or not he followed to the war to be a leader; tell what you know of gallant Peleus, whether he still has honor in the cities of the Myrmidons; or do they slight him now in Hellas and in Phthia, because old age has touched his hands and feet?
Achilles declares that if he could return to the earth just for a moment, he would want to come back and punish anyone who troubles his son or keeps his son from the honor he deserves. In other words, the way for a person to make an impact on the earth, to really make a difference, is through one's children. They are what bring a person happiness in death, when there is no other happiness to be had.
I tend to think that Odysseus' understanding of self regarding mortality is brought out in his discussion with Achilles. Throughout his journey in the underworld, Odysseus had been privy to many a story. All of them are connected through the thread that mortality had been extinguished. For Odysseus, his admiration of the power and awesome nature of Achilles, now a member of the underworld, triggers his own self- awareness about the nature of mortality. In a pointed exchange, the base for Odysseus' self- realization had become evident:
O shining Odysseus, never try to console me for dying.
I would rather follow the plow as thrall to another
man, one with no land allotted him and not much to live on, than be a king over all the perished dead.
For Achilles, life, even in the lowest of forms, is its own unique good. This is something that Odysseus begins to understand himself, a revelation that is completed when he quickly summons his men out of the underworld for fear of punishment or condemnation. The idea of being able to live life for what it is represents the epiphany concerning mortality that Odysseus gathers out his trip to the underworld. In Odysseus' understanding, life and the gift of mortality is something that cannot be squandered and the ability to return home to live it becomes a driving force, motivated by his epiphany.