Basically, the Great Depression hit Germany so hard that it (combined with lingering unhappiness over the Treaty of Versailles) made people lose all faith in the government of the Weimar Republic. In this context, President Hindenburg and others decided to turn to the Nazis for support.
As the link below tells us, Germany was hit very hard by the Depression. Somewhere around 33% of Germans were unemployed. Because of this Germans were very unhappy with their government. During this time, the Nazis became popular because they were not at all like the people who were in power. They were total outsiders and people thought that they might have a good way to get Germany back on its feet again.
Because the Nazis were gaining in popularity, Hindenburg and his advisers thought that making Hitler chancellor would win the approval of more Germans. They thought they could control Hitler and get him to work for them.
So, the Depression helped bring Hitler to power by making Germans extremely disillusioned with politics as usual and much more willing to take a chance on an outsider like Hitler.