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.
The Great Depression contributed to Hitler's rise to power in some ways, but mostly the Treaty of Versailles. The Treaty of Versailles took most of Germany's money and resources by making them pay for all damages caused by the war, and caused a mini-depression in Germany. Unemployment was high, inflation was outrageous, and most Germans were poor, out of work, starving, and depressed by Germany's loss to the Allies in World War I. They were so depressed that they would look to any leader who said the words they wanted to hear. When Hitler said he would return Germany to its former glory, and give everybody jobs, etc., everyone believed him, and no one suspected anything.