I'm not sure if you're asking about the causes of the Depression or of the crash of the stock market. The crash of the stock market starts the Depression going, but it wasn't really the cause. I'll try to talk a bit about both, but the causes of the crash are way easier and more agreed-upon than the causes of the Depression as a whole.
The stock market crash was caused by the prices of the stocks going up too fast -- much faster than they should have. This was caused in part by it being very easy for people to borrow money to buy stocks (called buying on the margin). So the stocks cost way more than they were worth and when this was realized, the "bubble" burst and the stock market crashed.
But the stock market crash wouldn't have caused a Depression if the economy had been stable beforehand. The economy wasn't stable. Some reasons that historians often give:
- Too much production of goods while workers were too poor to be able to keep buying them.
- Relatedly, too much concentration of income in the hands of the rich.
- The government didn't regulate banks and the economy in general as much as it does today.
But I have to emphasize that these are relatively liberal interpretations and conservatives and economic historians totally disagree with them.
There were several distinct causes of the Great Depression. Most of these worked in tandem with one another so that the mass combination caused the Great Depression. Obviously, the stock market crash of 1929 was an essential element in causing the Great Depression. The market was artifically inflated with purchasing power on margin or credit, and with this, there was no economic "there" there. This helped to inflate profits, creating purchasing on speculation, which invariable led to collapse. The failure of banks and the erosion of individual credit also helped to bring the economic machine to a grinding halt. At the same time, protectionist measures and a lack of effective trade with foreign nations in Europe also contributed to a lack of overall growth. Combined with drought conditions making agricultural profits plummet, this overall state of American economy ushered in the Great Depression of the 1930s.