The epigraph is taken from Dante's Inferno, the poem where Dante travels through the different sections of Hell. I found a translation of the lines online:
"If I thought my answer were given to anyone who would ever return to the world, this flame would stand still without moving any further. But since never from this abyss has anyone ever returned alive, if what I hear is true, without fear of infamy I answer you."
I think the significance is that Dante traveled through the depths of Hell and back, and while Prufrock's journey through Hell wasn't as literal as Dante's, he still had to weather the storms in life. There has been much debate on what, exactly, Eliot's poem is about, and to whom the speaker is speaking. I think the analysis I found on Wikipedia will help you out a bit, but as with all poetry, it's really open to interpretation. Hope this helps you!