It was one of the few times in US history where the vast, vast majority of Americans were united in a single political, economic and military effort. Almost every American family had at least one person serving in the military (16 million people overall were in uniform during that conflict), so we had an intimate connection to the war at the family level that we do not have today, since our military is now made up exclusively of volunteers, and make up only .4% of the total population. In World War II it was nearly 12%.
The war also shuffled the population of the United States, especially to the North and West. Large numbers of African-Americans moved to major cities for war industries, large numbers of women entered the industrial workforce, and the population of California and New York swelled.
During the war, one of the major impacts (on people who were still in the US rather than off fighting) was that the war made many consumer goods unavailable. There was a rationing system where people could only get so much gasoline or so much meat per week. This, of course, had a major impact on people's daily lives. Home economics magazines from the time, for example, are full of ideas about how to stretch one's ration to last longer. This is not nearly as serious as the impacts felt by the soldiers, of course, but it is a major impact on life on the homefront.
There were obviously many different effects but some of the major ones:
By creating an intense demand for manufactured war goods, the war had the effect of finally ending the Great Depression as factories went back to working at capacity and expanding and hiring large numbers of new workers.
It also created much more of a willingness to participate in international affairs, something that had been severely restrained after the end of World War I.
There were also significant effects after the war when GIs returned and went to college in record numbers on the government dime.