The Weimar Republic is mainly relevant in German history because of what it led to. While the Weimar Republic had some successes, its shortcomings (and its bad luck) made it possible for the Nazi Party to come to power. The rise of the Nazis and Hitler is, of course, one of the most important events of German history as well as of modern world history.
The Weimar Republic was born into crisis. It came about with the fall of the monarchy after Germany’s loss in WWI. The end of the war brought many problems. There were major economic problems which were exacerbated by the victorious Allies’ demands for reparations. There were political problems as extremists on both the right and left sought to destroy the nascent democracy. There was widespread unhappiness with Germany’s defeat and with the conditions that arose after the war. These conditions made it very hard for the Weimar Republic to succeed. It did manage to get Germany back on track to some degree for a while, but the coming of the Great Depression threw the Germany economy back into chaos, thus weakening the republic and allowing Hitler to come to power.
As to the constitution and democracy, we must realize that there is no clear dividing line between what is and is not democratic. Some systems are more democratic and some are less democratic. The Weimar Republic had a democracy, but its constitution left opportunities for undemocratic forces. The main opening was in the fact that the president of the country could appoint his chancellor. The chancellor did not have to be elected by the people. This allowed von Hindenburg to appoint Hitler even though the Nazi Party was not the most popular party in the country.
Once Hitler was in office, he was able to take many illegal actions to create a dictatorship. This could happen not because of flaws in the constitution but because the German people were not committed to democracy. The people allowed the Nazis to do things like suppressing the communists without really protesting. By suppressing the communists, Hitler was able to keep control over the parliament and he was able to get the parliament (the Reichstag) to pass various laws to give him complete power in a “legal” way.