This blog post was inspired by a question I was asked to answer on Quora by Robert Gluck, which consisted, in its entirety, of the phrase that makes up the title above. Herewith is my reply.
As has been pointed out by other respondents to this question, the phrase "the banality of evil" was coined by Hannah Arendt, as part of the subtitle to her 1963 book Eichmann in Jerusalem: A Report on the Banality of Evil. The book was her account of the 1961 trial, in Jerusalem, of Adolf Eichmann, who had worked during the Nazi era in Germany for branches of the S.S. dealing with "emigration," "relocation," and "evacuation" of Jewish populations across Europe. Many of these, of course, were convenient euphemisms for "extermination." By "banality," Arendt meant that, for people such as Eichmann who were part of the monstrous bureaucracy of death developed by the Nazis in the process of implementing their "Final Solution of the Jewish Question," dealing with matters involving the suffering and death of so many human beings became a mere matter of routine, "just another day at the office," as it were. (It is perhaps significant that Arendt herself later regretted employing the term, and noted that she would not use it if she were to write the book over again. By then, of course, it was too late, and had become a catchphrase.)
Eichmann, despite his many boasts to the contrary, was, it would appear, no more than a "middle manager" in this bureaucracy of death. He did not dictate the policies that were implemented; this was, of course, done, ultimately, by Hitler himself, and to a lesser extent by Heinrich Himmler, head of the S.S., and Reinhard Heydrich, head of the Reich Main Security Office, to whom he ultimately reported. Nor did he actually kill anyone; in fact, the one time he visited sites where the actual killing of Jews happened (once by firing squad, once in the gas trucks), he was sickened and shaken by the experience. Eichmann's chief concern was that of transportation, shifting Jews around from location to location, locating the trains needed to move them and making sure there were enough people aboard each train so that no trains were "wasted," and ultimately delivering them up for "resettlement in the East" (read: extermination at Auschwitz or one of the other death camps). He may have viewed the lives affected by these operations as no more than abstractions, numbers which had to be shifted around to meet the expectations of his superiors. (A similar attitude is expressed in a quotation famously misattributed to Joseph Stalin: "The death of one man is a tragedy. The death of millions is a statistic." )
Edward Herman calls the development of this "banality" a process of "normalizing the unthinkable," in which, over time, terrible, murderous acts simply become "the way things are done." This was certainly the case for Eichmann as he was made responsible for the "relocation" of Jewish populations throughout Europe. The example of Rumania is perhaps relevant here: the Rumanians were so eager to comply with Nazi demands that their land be made judenrein (Jew-free) that they instituted their own bloody pogroms against their own Jewish population. Eichmann was forced to scramble, quickly arranging transportation so that the Rumanian Jews could be dealt with in the usual fashion. Even though the outcome was ultimately the same, he felt that the approach taken by the Nazis, the "way things were done" to which he had become accustomed, was more "civilized."
It's also true that people in this kind of situation may not be aware of the ultimate consequences of their actions, though Eichmann, at least in the latter half of his career, surely was. This may include, not only those such as the Nazis, but scientists involved in the development of potentially-destructive new weaponry. In the movie Real Genius, for example, Mitch Taylor and Chris Knight are college students engaged in developing a powerful laser merely as a research project for Professor Jerry Hathaway. After they succeed, and Lazlo Hollyfeld confronts them with the question "What would you use that for?", their friend "Ick" Ikagami deflects the question with a joke ("Making enormous Swiss cheese?" ), Knight brushes it aside, thinking only of his own situation ("Lazlo, that doesn't matter! I respect you, but I graduated!" ) and Taylor shrugs it off: "The applications are unlimited...let the engineers figure out a use for it, that's not our concern!" Only when further prompted by Hollyfeld, and upon returning to the lab to find out their laser has been spirited away for immediate military testing, do they realize the enormity of what they've done and begin working on a plan to sabotage it. Whatever "evil" they committed in the design of what proved to be a new weapon surely was "banal" in that sense, and acquired this quality chiefly by virtue of their own ignorance. The real evil, it might be argued, was Hathaway's, in exploiting their labor without informing them of the ultimate purpose, after having diverted funding for the laser project towards remodeling his house. This mirrors the way the Nazis engaged in division of labor to keep groups of people in their lower echelons focused on minor details of the Final Solution instead of on the "big picture"...and corruption was also endemic in the Nazi era as well.
Friedrich Hayek, in his book The Road to Serfdom, wrote, "Advancement within a totalitarian group or party depends largely on a willingness to do immoral things. The principle that the end justifies the means, which in individualist ethics is regarded as the denial of all morals, in collectivist ethics becomes necessarily the supreme rule." This is a contributor to the development of evil as a "banality," if it is viewed as something that one is merely required to do to maintain and advance one's position, such as Eichmann hoping for advancement in his post, or Knight getting his college degree. People are often willing to "go along to get along," as shown by Milgram's experiment and Zimbardo's Stanford prison experiment, as well as by the Jewish Councils set up by the Nazis, which did much of the "dirty work" in selecting those who would be put on the trains for "resettlement," perhaps in the belief that they would avoid the same fate or worse thereby. (Ultimately, this would not be the case; many members of the Councils themselves were sent along to the death camps.)
So we have a number of conditions: the participants in evil acts are either ignorant of the consequences of their actions or are willing to suppress or "abstract away" what knowledge they have of them, their actions have been "normalized" by the organization they work in, and they view their actions as necessary to maintain or advance their own position, or to further their own goals. Under these circumstances, yes, evil can become quite "banal" indeed. It is worth noting, in closing, an observation that Isaac Asimov once made in recounting a conversation with Fritz Leiber: a truly "intelligent" villain never just shouts "I'm a wicked bad guy!", he is never a "villain" in his own eyes. Eichmann certainly was not; he even professed that he had been trying to save Jews by his actions, even as he acknowledged that he was to be made something of a scapegoat for the Nazi regime by his trial and execution. Even one of the most clichéd villains of all time, Darth Vader, would tell Luke Skywalker that his ultimate aim was to "bring order to the Galaxy," much as the Nazis wanted to bring "order" to the world. Their examples must stand as a cautionary tale for us all.