USSR began building missile sites in Cuba in 1962.
There was a coup in Cuba in '59. The new government did not like the United States and took over some American businesses.
The missle sites could hit any city in the USA.
American ships blocked Soviet ships carrying misses into Cuba. The Soviets and Cubans agreed to take away the missiles if America promised not to attack Cuba.
Technically, nobody won. Although, the USSR lost China's support after.
In this excerpt, the word tension means discomfort. Dr. King is saying that a certain level of discomfort is necessary for growth as a country. The group(s) that have been oppressing the black community are to expect nothing short of discomfort. Facing difficult emotions is the only way that we, as a community, can make any sort of change.