The answer to this question will depend on whom you ask because there are many different types of historians who specialize in society, politics, and the economy. The Red Scare that took place during the early part of the decade was one of the most important events of the decade. Americans were afraid of a Bolshevik takeover of the government. Someone detonated a bomb on Wall Street in 1920. The government and public opinion started to crack down on anything that looked like anarchism, Bolshevism, or Eastern European influence. The United States deported hundreds of socialists, most notably Emma Goldman, to the Soviet Union. The United States also killed Saaco and Vanzetti for their role in a Massachusetts robbery, but the real crime was their alleged anarchist ties.
The United States passed the National Origins Act of 1924, which severely limited immigrants from Southern and Eastern Europe at a time when those regions needed sanctuary in the United States the most. The Red Scare and the strong nativism that resulted from it played a big role in American cultural and political history.
The booming stock market also transformed the country in the latter half of the decade. People considered themselves rich though much of the money was on paper only—the agricultural sector still lagged behind most of the country economically as farm prices dropped after WWI. When the stock market fell due to overspeculation, it was the beginning of the Great Depression.
Of course, you can pick different events, but for me these are the events that shaped the decade.