Eliot alludes to Dante's Inferno, Dante's account of his journey through Hell under the guidance of the spirit of the poet Virgil, in order to highlight the banality of Prufrock's frustration and despair. This allusion works in both a general and a specific way.
As a general allusion, the quotation contrasts Dante and Prufrock. Dante, in his poem, is a fearless seeker after the truth about himself and others, who has literally gone to Hell and back in his quest. Prufrock, on the other hand, cannot even make up his mind about ordinary life:
Do I dare
Disturb the universe?
In a minute there is time
For decisions and revisions which a minute will reverse.
He whines that he "is not Prince Hamlet, nor was meant to be," and sadly concludes that the mermaids will not "speak to me." The evocation of Dante shows him clearly to be an empty, querulous nonentity.
The specific allusion that Eliot chooses quotes the words of one of the sinners in Hell, Count Guido da Montefeltro, who tells Dante that he would never speak if he believed that Dante could ever take his words back to the living world. For those who understand Dante's text, this serves to further underline Prufrock's inferiority. Prufrock is part of the world, not condemned to Hell, but he is as isolated and impotent as the damned: "It is impossible to say just what I mean!" He can never make up his mind to ask his "overwhelming question," and is convinced that he is "ridiculous" and "the Fool."
Thus, on both the specific and the general levels, the contrast between Prufrock and Dante makes the former, and by extension his times and his society, appear pathetic, irresolute, and contemptible.