Outside of the fact that there was a presidential election that year, there was nothing particularly special about 1968 that made so many things happen in that year rather than in 1967 or 1969. Most of the upheaval that happened in that year happened simply because the late 1960s were a tumultuous time. The major factors behind this tumult were the Vietnam War, the Civil Rights Movement, and the Counterculture.
There were two events that happened in 1968 that were largely possible because it was a presidential election year. These were the killing of Robert Kennedy and the violence at the Democratic National Convention in Chicago. The convention chaos was caused by the general tumult of the ‘60s but it took place in 1968 because of the election. Kennedy’s assassination was more of a random event, but it would not likely have happened were it not for the election.
The other things that happened in this year happened because of the general upheaval of the era. Martin Luther King, Jr. was assassinated because of his involvement in the Civil Rights Movement. His killing, along with the fact that the movement was sputtering to a halt even before he died, led to the riots that happened in various cities. The Tet Offensive happened because the US was involved in the Vietnam War.
In general, then, the upheaval of 1968 happened because there was a lot of upheaval in this time period as a whole and because of the presidential election.