Contrapasso is the correspondence between the punishment and the sin: the punishment describes what the condemned did in life, instead of punishing him from outside. The word appears only once in the poem, in Canto XXVIII, on the lips of Bertran de Born, but the logic holds for the whole of Hell.
Bertran de Born carries his own severed head, like a lantern, and says: because I divided persons so closely united, I carry my brain divided, far from its origin, which is in the trunk. Thus, he says, the contrapasso is observed in him. He separated father and son, and now he is separated from himself.
The same logic appears elsewhere. The lustful, who subjected reason to desire, are carried by a windstorm without rest. The soothsayers, who wanted to see too far ahead, walk with their faces turned backward. The hypocrites, gilded outside, carry leaden cloaks within. The thieves, who took what belonged to others, lose their bodies, which circulate from one to another among serpents. The fraudulent counselors burn each within a flame that hides him.
That is why no one there repents: each condemned man goes on wanting exactly what brought him there. And the fact that the word comes from the mouth of the one who most fully carries out the law to the letter shows that the justice of Hell is something the condemned understands and confirms, and not merely suffers.