First of all, we must be careful not to say that the stock market crash caused the Depression. It is more accurate to say that the crash was something of a catalyst that upset an economy that was already fragile. It was the underlying fragility of the economy that caused the Depression.
Historians typically blame overproduction in the industrial sector and a poor distribution of wealth for the fact that the economy was fragile. They say that American factories produced too many goods during the 1920s relative to what consumers could buy. The workers were not making enough money to buy all of the things the factories produced. The wealth was concentrated in the hands of a few.
Even before the crash, consumption was slowing. When the crash came about, consumption dropped even further. When this happened, more and more people were put out of work. As more people lost their jobs, consumption dropped even further in a vicious cycle. This led to the Depression.
The Depression then got even worse with some of the measures taken to end it. The worst of these was the Smoot-Hawley Tariff. When the US erected trade barriers (as did other countries) trade was choked off and there was even less of an outlet for US goods. This, of course, led to further job loss.