The Shoah, or the annihilation in Hebrew, is the name jews use for the Holocaust. More precisely, to the part of the holocaust that includes the mass killing of millions of jews, and their gathering in concentration camp - an experience the few survivors have difficulties to tell about.
The Shoah was the doing of the Nazis, whose antisemitism led them to power. Once they ruled Germany, and after 1940 most of Europe, they decided to eliminate the jews living there, using such tools as the gas chamber, or more quickly with a bullet behind the head, the way most common in Eastern Europe.
About 6 million jews had disappeared after the war. But it was not easy for those few who survived. They had seen their family die, or did not know their fate. Also, given the way a concentration camp worked, they often felt guilty for surviving : the goal of such camps as Auschwitz wasn't only to quickly kill thousands of people each day, but also to make sure those still alive somehow lost their humanity, by having them fight among themselves for life. So those who survived were depressive, or tried to negate their experience, or couldn't live with it... Primo Levi, who has written some of the best litterature about the Shoah, comitted suicide.
It has been wondered if it was possible to make art, in a society that had made the Shoah possible, as it was clear it had no redeeming effect - The Nazis were fond of fine works such as Wagner's. However, many people have tried to tell of the shoah, including the aforementioned Primo Levi, Georges Perec, Steven Spielberg...
Many people belonging to other minorities were killed at the same time. But "Shoah" is more specific to the jews