In the poem, the speaker, J. Alfred Prufrock, seems to be describing his desire to ask the woman he's with if she can love him, if she does love him. He points out all of his shortcomings—his baldness, his timidity, his thin legs, his feeling that he is not enough or that he is hopelessly wrong—and reports that he would like to have "the strength to force the moment to its crisis." At the same time, he feels "presumptuous" for even considering asking the question he would like to. He is "afraid," very afraid that, if he asks his question, the woman will say "That is not what I meant at all; / That is not it, at all." He fears rejection, but he also fears making a further fool of himself, though he seems to feel that such a thing is essentially inevitable. He is "not Prince Hamlet," he says, but rather, "the Fool."

As others have pointed out, the epigraph is a quotation said by a man named Guido who is in the eighth circle of Hell in Dante's Inferno. Guido thinks it's safe to tell Dante his story, and so Prufrock likely believes it is safe to share his story with us. For Guido, it is because he thinks that none can escape Hell, and this allusion would seem to characterize Prufrock's reality as a kind of Hell in which he believes everyone is stuck too. Prufrock really does seem to feel stuck in Hell—one created both by his society as well as by his own fearfulness—and so he speaks to the reader as another who is also trapped in this same hellscape as he.

The epigraph is from canto 27 of Dante's Inferno. At this point in their tour of hell, Dante and Virgil are in the eighth circle, where some of the worst sinners reside. Dante comes across a man named Guido and asks him what he has done. Guido responds with the quote in the epigraph that in English translates as the following:

If I thought that my reply were given to anyone who might return to the world, this flame would stand forever still; but since never from this deep place has anyone returned alive, if what I hear is true, without fear of infamy I answer you.

Guido, who has turned into nothing but a wavering flame, believes his confession is safe with Dante because Guido thinks that no human can return from the underworld. Even in hell, he is concerned with his reputation on earth. Ironically, Dante will return to earth and reveal Guido's sin in his poem.

This relates to the "overwhelming question" because Prufrock is going to, like Guido, reveal his secrets to us, thinking it is safe to do so. The overwhelming question is, on one level, the question he is debating, which appears to be whether to propose marriage to the woman going with him to the party. But the overwhelming question is more ambiguous than that: it is more universal than a marriage proposal. Prufrock wonders if he should have put his all into answering the "overwhelming question" of the truth of life.

But Prufrock's confession is that he has not put his all into life. He has frittered his talent away at parties. He has been paralyzed by timidity and indecision. He has never made the great leap of faith to tell his truth but instead has settled for being second rate. He will never do anything creative and daring, whether it be to propose marriage to a woman or write a great poem. And like Guido in the epigraph, he wants to hide this truth about what he is from others.

Scholars and critics alike agree that the "overwhelming question" that is the focus of all of Prufrock's ponderings in the poem is most likely a marriage proposal, or a question of a woman's feelings for him.  He obviously cares for a woman, is intimidated by her, has spent time with her, and wants to speak his heart to her.  He either wants to propose and get an answer, or to reveal his love for her and have her reveal how she feels for him. If anyone has been in a situation where they care deeply for someone but are unsure of that person's feelings for them, they can relate to his paranoia, obsession and fears in regards to the subject.

The poem opens up with a reference to Dante's Inferno; it speaks of a man asking for forgiveness before he commits the crime that he has in mind.  This can be tied to Prufrock's question, because he wants to be able to guess the woman's answer before he ever asks the question.  He doesn't want to ask the question unless he can be reassured of her positive response; if he asks, and gets a negative response, it will be too devestating for him to handle.  He wouldn't recover.  Just as Dante's lines states "since no one has ever returned alive from this depth," Prufrock fears that he won't ever be able to return alive after receiving a negative answer from her.  He fears her answer; the entire poem is him trying to get up the courage to ask her, but he fears that once he has "disturbed the universe" she will just, as he puts in the poem, sigh, and say, "That is not what I meant at all/that is not it, at all," referring to his supposition that she cared for him.

In the end, he decides it's not worth asking.  It's not worth risking a no from her, a rejection of him.  He chickens out, and resolves himself to the fact that he is a bit of a coward, and that he will forever be one of those people who looks on and longs from afar, but never partakes of the joys that he craves.  I hope that those thoughts helped a bit; good luck!