There were at least two major transformations in American politics during this time, one domestic and one foreign.
In domestic politics, the United States became much more conservative during this time. The 1970s had been a relatively liberal decade. President Nixon was a Republican, but he was very much a liberal compared with Ronald Reagan. By the late 1990s, the American domestic political scene had changed so much that Bill Clinton won two terms in office as a Democrat who did very centrist things like reforming welfare.
In the international arena, the major change had to do with the end of the Cold War. In the late 1970s, tensions were relatively high with the Soviets having just invaded Afghanistan. These tensions continued to rise through the 1980s. However, the Soviet Union then collapsed at the end of the decade. This completely changed American foreign policy. Instead of having to focus on containing communism, it was more interested in keeping the peace in the world as a whole. The US was now the only superpower and it had to do things like trying to keep peace in the Balkans and ejecting Iraq from Kuwait after the Iraqi invasion of 1990.