In a nutshell, Levinas talks about responsibility and the other as an enigma. His concept of the human being as an enigma, or as a puzzle shatters the fatalistic image of Dasein in Heidegger's works. We are not simply beings going towards death. Humans are like puzzles or mysteries whom one cannot fully determine or reduce as an object. In other words human beings, or the others, are full of surprises. And this enigmatic characteristic of the other is the basis of his advocacy of responsibility. Being responsible for the other is a sign of respect. It is how an individual recognizes the other's subjecivity and the limitlessness of their possibilities. This sense of inexhaustible potential does not only lift the limits of what the other can do but also what the other can become. It gives a sense of chance, hope and belief in the growth of an individual. It recognizes the possibility that a criminal can change for the better or that a corrupt leader can be convinced to work for the prosperity of a nation. We have no right to objectify and box-in an individual because we simply cannot have a hundred percent certainty on what they are capable of. Unfortunately, Levinas is silent on how long before these changes could take place. It is not question of when but how.
The philosophy of Levinas is truly an attempt to criticize the works of Heidegger. Despite our common destiny of dying, it is not an excuse for us to disregard our relationship with the others and their personhood. Well, that finally restored my confidence in humanity but Levinas wasn't enough to repair the damage Heidegger did. It was just a shame that he said nothing about religion... at least, not in our lectures.