There could be many answers to this, with different answers for domestic affairs and foreign affairs.
The most important thing that characterizes the Kennedy years, in my view, is foreign affairs. Kennedy's short term in office was quite eventful in foreign affairs, particularly in terms of the Cold War competition with the Soviet Union and communism in general.
There were at least three major events or areas of importance. The first two have to do with Cuba. These were the Bay of Pigs invasion and the Cuban Missile Crisis. The third important area was the increasing involvement in Vietnam.
All of these events had to do with the US trying to prevent the spread of communist power across the globe. This Cold War issue was very characteristic of the Kennedy years.