It began an era of unprecedented prosperity - we got out of the Depression and hardly looked back.  Because of our new wealth, middle class jobs, homes in the suburbs, socially we became an extremely materialistic society.  In the 1950s, we also became much more conformist as those who had survived the Depression and World War II just wanted to live the good life.  Their kids, the baby boomers, had trouble believing that was all it was about, and the roots of the counterculture started with them.

There are many things to write, but here are a few:

1. America entered into a time of great material prosperity.

2. America entered into a time of trust in the government. WWII was seen for the most part as a moral victory against evil. Hence, people felt that it was right to fight in this war. This would be shattered in Vietnam.

3. America also embraced technology more and more and technology would increase.

4. America also saw the burgeoning of the civil right movement, which would have enormous repercussions.

5. Finally, in all this prosperity, there was a sense of the lack of meaning. Think of the music and movies of this time. The seed of wanting something more was sown.

The postwar period from 1945 to 1965 in the United States was a time of intense change.  Economically, as has already been stated, the US was the only industrial power undestroyed during the war;  this lead to unprecedented economic growth for this period -- indeed, it was only in the late 1960's and early 1970's that Europe and Asia got "back up on their feet" and could compete with the US in heavy industries, like automobile manufacturing. Although its been perceived that the US economy slid by the 1970's, what really happened was that the rest of the world caught up.

Socially, the dislocations that the war caused were, for a time, put aside, as if everyone wanted to "return to normalcy."  With the men returning from the war, women returned to the home, and the "Baby Boom" began.  Those 77 million children born in those years represent the largest demographic block the US has, and probably will ever see.

World War II was destructive on many fronts, politically, economically, and socially.  The first two were felt immediately; the last took until that first postwar generation came of age.  Having had no ties to how it was before the war, and comparing their own experiences to their parents, who had endured the difficulties of the Depression and the war, many felt older generation's focus on the accumulation of wealth to be the cause of current problems.  Compounding the differences in opinion between parents and children was the US foreign policy, which engaged Korea and Vietnam.  The Vietnam War, in particular, exacerbated this rift between young and old and created the "Generation Gap."

The previous response hit nicely on the idea that no answer to this question could be effectively conveyed in this forum.  One critical way in which the nation changed both economically and socially is through the confidence professed in free market capitalism and democracy.  The years leading to World War II brought much doubt in both.  The resolution of the war and the staunch opposition to the Soviet Union convinced the nation to forcefully and zealously embrace both the free market and the democratic notion of the good.  In the process, this embrace of a comedic vision of harmony and unity started to give way to competing notions of the good which were voiced by individuals who demanded to be included in the post War vision of America.  It is through this dialectic where we are able to see the narratives of people of color, of the poor, and of women to emerge into the discourse.  Following this were the visions of those who wished to have their realities of sexual orientation to be integrated.  Such inclusion helped to make America within the 20 years after the Second World War a different nation than the one that claimed victory against the Axis powers.

With the administration of the greatest general of World War II, Dwight D. Eisenhower, as president of the United States, the country knew 0 inflation.  After soldiers returned home, in 1946 the "Baby Boom" began and the construction of homes also boomed.  The parents of the "baby boomers" were frugal.  Having lived through the Great Depression, these people distrusted banks and buying things on credit.  Therefore, they saved and paid cash for whatever they wanted, unless absolutely necessary, as in the case of the purchase of a home.  Their values and ethics were above reproach; "one's word is one's bond" was repeatedly spoken.  People were decent with a respect for their neighbor's natural rights.  There was little need for the police to patrol many neighborhoods.  The majority of men worked for a living; since inflation was so low, mothers could stay home and raise the children, even if they had worked during the war.  Prevalent in this age was decency and the work ethic.

In the 1960s the "Baby Boomers" went to college, often the first of their families.  At the universities, these young adults were exposed to the liberal and often radical ideals of professors, much unlike the thinking of their conservative parents.  Influenced by new ideas and rebellious against the almost fearful conservatism of their Depression parents who seemed concerned only for their own welfare, these students joined radical groups such as the Students for a Democratic Society (SDS).  This group was active in the civil rights movement, but later became active in anti-VietNam War protests.  The SDS often coordinated activities with the Black Panthers and espoused radical, though at first Marxist, means of protest.  A splinter group, known as the Weathermen believed in violent revolution and acts of terrorism to achieve their goals; this group was implicated in a number of bombings at colleges and federal institutions.  Another radical group, the Yippies, was responsible for disrupting the Democratic Convention for President held in Chicago with their candidate Pigasus. The Yippies, whose leader was Abbie Hoffman, caused the ensuing riots in the Second City.

Of course, the Civil Rights Movement of the 1960s was extremely consequential to the country. Economically, jobs were opened to minorities with the Civil Rights Act of 1964 as President Johnson ordered "affirmative action," and desegregation dramatically changed the South socially as well as major cities in the North in which forced busing was enacted, changing the demographics of public schools.  Indeed, life in the United States was altered dramatically in the I960s. Having socially altered the U.S., the Baby Boomers also began the consumerism that is prevalent today.

A full answer to this would take at least a few books...  So here's a really brief one:

The two decades after WWII were a time of unprecedented (before or since) economic boom in the US.  The US was the only developed nation untouched by the war and so it was able to have a huge advantage over the rest of the world.  This was a golden age as US standard of living grew.

Socially, the two decades are way different.  The '50s were the time of people soberly working hard, making up for time and opportunities lost during the Depression and the War.  The '60s were the time when those people's children came of age and started huge social upheavals.

That's a really quick and dirty summary...