The 1932 presidential election had the incumbent Republican, Herbert Hoover, running against Franklin D. Roosevelt, the Democrat. This was the first presidential election of the Great Depression. The contest revolved mostly around the two men's ideas for ending the Depression.
The caricature of Hoover is that he did not want the federal government to do anything to end the Depression. This is not quite true. He wanted the government to act to end the Depression, but he did not think that it should do too much. He wanted to take a relatively cautious approach, doing things like lending money to businesses and providing a few jobs on things like the Hoover Dam.
Roosevelt had a much more expansive role for government in mind. He promised a "New Deal" in which the government would take more kinds of actions to end the Depression. To FDR, the government needed to do things like encouraging businesses to work together to set standards and wages (the NIRA). It needed to do things like reducing the amount of agricultural products that would be produced (the AAA). It needed to do things like providing income security for the old (Social Security). The government, then, was going to do many more kinds of things than Hoover wanted.
Hoover wanted the government to do some things (but not too many) to help end the Depression. By contrast, FDR wanted the government to do many different kinds of things. This was the major difference between them in terms of the role of the federal government.