What separates a genocide, e.g. the Shoah, from a numerically equivalent or, indeed, greater mass murder?
Her answer, which is the most concise and illuminating I've read, is an explanation of the phrase "crimes against humanity," which she would have us rephrase "crimes against the human status." Genocide attempts to deny cultural diversity, which is one of the central facts of the cohabitation of humanity on Earth, as well as of the human status. It attempts to deny the capacity of different groups to define their own space and their own relations to each other. Genocide, especially when as in the Shoah it is part of a general genocidal worldview, is an attempt in the end to make genuine human interaction impossible by destroying the Other facing which we ought to interact. Of course such crimes are made particularly horrendous by being attached to mass murder, but there are other ways the aim can be achieved. One thinks of language death.
"Tout comprendre, c'est tout pardonner." Mme de Stael. To understand is to forgive. While the phrase is a commonplace, it seems no less true that, at the point when one can tell oneself "I would have done the same" one has forgiven (regardless of whether one would forgive oneself had one done the same) because one feels incapable of judging. On the other hand, the truly incomprehensible (e.g. the psychopath) causes revulsion but not true condemnation. How, then, is it possible to judge?
Arendt finds in present-day society an unwillingness to judge individual actions or people, an unwillingness to render verdict or punish. To her, this marks the abandon of justice. The word justice, indeed, is her answer. That justice must be served is self-evident, and for this we must judge, despite our frailty.
The difficulty for the judge is that he must accept the irreducible strangeness of the other person while attempting to understand. He must accept that there was a choice and therefore responsibility and therefore something to judge - and he must be willing to say "there but for the Grace of God go I."
There. I've butchered Arendt enough. I find her work endlessly fascinating and troubling, and difficult to summarize or tighten up. Which, of course, it should be.