The conflict in The Devil's Arithmetic comes from two different sources: Hannah herself and the Nazis in the flashback scenes.
In the present day (the 1980s, when the book was written), Hannah is unable to fully comprehend the significance of the horrors of the Holocaust for her grandparents. Having grown up without experiencing the severe persecution they experienced during World War II, Hannah cannot comprehend how the Holocaust affected those that came before her.
While Hannah cannot help having a more privileged upbringing, she lacks compassion or understanding. She eventually overcomes these flaws during her experiences in the concentration camps, even choosing to die in Rivka's place. By sacrificing herself (all the while not knowing she will be returning to her comfortable life in modern New York), Hannah demonstrates that she is no longer the naïve, ignorant girl she was at the start, but a kinder, wiser person who can now better connect with her grandparents.
The other major conflict comes in the sections in the past: the Nazi persecution of the Jewish people. This conflict is more exterior than Hannah's having to overcome her inner emotional blocks. The Nazis round up the Jews and put them into concentration camps where they are enslaved, tortured, and killed in gas chambers. In the context of the novel as a whole, this outer conflict both provides suspense and prompts Hannah's character development.