The Nazis killed Jews as part of what they called the "Final Solution to the Jewish Question." In the ideology of the Nazis, the Jews were negatively described as an inferior race, which, in their opinion, was responsible for many of the problems of Germany and Europe in general. The Nazi Party promoted anti-Semitism, that is, hostility towards the Jews, from the very beginning of its existence.
When the Nazis came to power in Germany in 1933, they began introducing laws restricting the rights of Jews. Over the next few years, these laws became increasingly cruel and oppressive. In 1938, the so-called "Night of the Long Knives" was held, when the Nazis staged a series of attacks on Jewish areas, killed and beaten Jews, and sacked their shops and synagogues.
In 1939 World War II broke out and the Nazis took over most of Europe, including the Jewish communities in the territory they controlled. The Nazis began mass killings of Jews in specially organized death camps such as Auschwitz-Birkenau, Treblinka, Sobibor and others. In total, about 6 million Jews were killed during the Holocaust.
Thus, the Nazis killed Jews because of ideological beliefs that held Jews responsible for their country's problems, and used this as a justification for their genocide.