Although there have been several in American history, I infer you're referring to the crash in October of 1929. Much of the direct cause can be attributed to over speculation -- stocks are subject to the same economic law of supply and demand as any other commodity -- in the 1920's, the US surpassed Europe as the primary economic force in the world, primarily because the economies of Europe imploded during and after World War I. As the only substantial industrial power left, the US saw its economy expand, leading to the phrase that defines the era as "The Roaring Twenties." With increased wealth, many more people began to invest in stocks, driving up the price. Concurrently, unscrupulous investors, like JP Kennedy (patriarch of the Kennedy Clan,) made millions by "Stock Pooling," where a group would pool their money to buy stock, drive up the price, and once enough other investors not part of the pool had bought in would sell shares all at once. This guaranteed a huge return to the original investors at the expense of the later ones. Unfortunately, Kennedy and others began to move larger and larger blocks of stock in and out of the market, and as wider and wider price swings of high and low for a given stock occurred many investors began to stop investing and liquidate stocks, causing prices to fall, then tumble, then crash. Ironically, Mr. Kennedy was made the first chairmen of the SEC (Securites and Exchange Commission) under President Roosevelt (FDR) to curb the abuses he himself had instigated! The president offered the job to Kennedy and stated, "It takes a thief to catch a thief."
When we start talking about stock market crashes, like the one that helped spur on the great depression, the main idea always becomes one thing: loss of consumer faith.
When consumers stop believing in the power of their dollar, the market suffers as a result. The only thing that "backs up" our money, one must remember, is sheer faith. Our currency system works like this: a dollar is worth one dollar, not because it's backed up by that amount of gold or other assets, but because we as consumers recognize its value as one dollar. We do not operate on the gold standard or any other similar system, but rather, believe that our money is worth what is says it is. When that faith wanes, disastrous outcomes, such as stock market crashes, can occur.