In my opinion, the two most important aspects of the legacy of the Second World War are:
1) The degree of human suffering experienced in WW2 was unmatched in history. During the war, carpet bombing campaigns targeted civilian targets as much as military ones, while starvation and disease claimed a stunning number of lives. Atrocities also added misery; the Holocaust alone killed 11 million people, half of which were Jews.
2) WW2 had only just ended when the world plunged into another conflict. In Europe, a rift grew between the uneasy alliance of capitalist and communist philosophies, splitting Europe into two, divided by the "Iron Curtain". Because the two dominant powers of the post-WW2 era, the United States and the Soviet Union, never directly fought an open war, the term "Cold War" was coined to describe the tension and rivalry between them. The two powers did, however, engage in proxy wars such as Korea and Vietnam.