I think this is an excellent question, because it's very difficult to give an objective and concise explanation for the Second World War, never mind to a younger audience.
Perhaps this may work, by focusing on both the big picture and the beliefs behind the conflict. The answers so far have also not mentioned much outside of a European or American context. I hope the below deals with themes general enough to be applicable to broader moral lessons and historical examples. Focusing on Hitler and declaring the problem his lone "insanity" I think is dangerous morally and intellectually.
Germany, Italy, and Japan believed that conquering their neighbours would prove they were better than everyone else. Many Germans thought they had been treated unfairly, and blamed others for their problems, especially the Jews. But blaming Jewish people and thinking themselves the best was wrong. When people think they are better than everyone else, they start to treat other people badly.
From 1939-1945 the world was in a war between the Allies and Axis. The big four Allied powers were China, the British Empire, the Soviet Union, the USA. The big three Axis powers were Nazi Germany, the Kingdom of Italy, the Empire of Japan. Many more people were with the allies. Belgium, the Netherlands, France, and Poland, for example, tried their best to defend against Germany, but were conquered.
Millions of people died, many of them were innocent. In the end by putting aside their differences and working together, the Allies won the war. But it was too late for many people, like those who were murdered in the Holocaust. Because the Germans believed the Jews were to blame for their problems, they thought that if they killed them it would solve their problems. They murdered families. Men who could fight, old people who could not, even children like you, even babies.
This is why you must not be mean to others. The more people who think it's okay to be mean to someone because they are different, the more likely it is someone will get hurt. When everyone thinks it's okay to blame people because they are different, it becomes easy to hurt them, even if they're completely innocent.