Why did they do the book burning of 1933?

Hitler and the Nazis were beginning their campaign of demonizing anyone they disagreed with. This meant Jews, as well as intellectuals and political dissenters. The book burning was designed to stir up outrage against "dangerous" or "unpatriotic" books, as well as against the people who wrote such books. (It should be noted that none of the books were really dangerous, except perhaps to people like Hitler; but for Nazi ideas to dominate, the Fuehrer and his Propaganda minister Joseph Goebbels needed to persuade the public that certain books deserved to be burned. This event and others like it seem to have succeeded.)

Most dictatorships, Hitler's included, start by controlling public opinion and making sure the average person only reads or sees information that reinforces the dictator's core message. Hitler used events such as the book burning to begin a process of persecuting Jews and intellectuals, and persuading the public that supposedly anti-German ideas would not be tolerated.