It's very unlikely that the average person in the Great Depression would have understood much about the larger ramifications of the stock market or what it meant.

This was one of my major qualms with Amity Shlaes' book Calvin Coolidge, which claims that the increase of the DJIA during the Coolidge administration shows how great of a president she was. (Rather than consulting unemployment numbers like other historians, she cites the DJIA, which is also cited here from Eric Rauchway, a professor at University of California Davis.

To further give credence to this claim, I would turn to the following numbers from Shmoop

Number of millionaires in America at time of stock market peak in 1929: 25,000- 35,000

Number of millionaires in America at time of stock market bottom in 1932: 5,0006

Percentage of Americans who owned stock at time of 1929 Crash: less than 1

With such a low percentage of Americans owning stock in 1929, it would seem inaccurate to claim that Americans had much more idea about stocks then than today, other than in a vague, distant way. For workers then, the direct ramifications of the Great Depression were much more severe: while we mostly remember the stock market crash of 1929, unemployment in fact peaked two months earlier in August.

Then, as always, the poor and uneducated understood less about the abstract concepts of the economy than about whether or not they had food, a roof over their heads, and clothing on their bodies. The foot-dragging of the federal government, first in reacting to emergencies under Coolidge, later in enacting legislation to curtail the Great Depression under Hoover (a period I have not yet studied much) and even mismanagement at times by FDR resulted in a panoply of diverse opinions, as the reaction to such moves as the wasting of six million pigs shows. Hopefully not too tangential.

Sources:

Conrad Black, Champion of Freedom: Franklin D. Roosevelt

Amity Shlaes, Calvin Coolidge

H.W. Brands, Franklin D. Roosevelt

Mitch Hiltzik, The New Deal: A Modern History