Simple definition: The Nuremburg Laws were anti-Jewish regulations that excluded German Jews from becoming citizens in the Nazi Reich. Additionally, it also prevented Jews from marrying or laying with German or German-related (and obviously non-Jewish) blood.
To be classified as a "Jew" in Nazi Germany, you could be born of Jewish parents or even have just three or four grandparents who were Jewish/belonged to the Jewish community. Even Germans who had not practiced Judaism, but had family who were Jewish, found themselves subject to the Nuremburg Laws and later Nazi extremism. The law also applied to anyone who had Jewish grandparents that later converted to Christianity, because initially they were born of/practiced Judaism.
The Nuremburg Laws fueled anti-Semitism in Germany, encouraged anti-Semitic propaganda, and resulted in an increase in German-on-Jew violence.
The Laws were published on September 15, 1935 and read by Reichstag President Hermann Goring, who was an important figure in the Nazi party during WWII. It was billed as a "Law for the Protection of German Blood and German Honor", as Hitler and the Nazi party considered Jews the "mortal enemy" of the German People.