The German Republic (1918-1933) was a federal semi-presidential republic. It was ruled by a president that selected a chancellor with the "confidence" of the Reichstag. The Reichstag was elected by Proportional Representation.
The reason why this eventually led to the Nazi dictatorship was that Weimar couldn't have a stable government because of the proportional representation leading to coalitions that didn't last long. Even the Nazis were forced to rely on coalitions at first. That probably was the reason that they decided to burn the thing down.