On October 23rd, Russian ships approached Cuba. Tension began to build on both sides and the world went silent. Both sides had enough nuclear weapons to destroy the earth 4 times. This could be the start of a nuclear war? On the 24th October, even though the soviet ships were closely approaching the border of Cuba, Khrushchev ordered the Russian ships to turn around. Khrushchev knew the consequences of sending the ships there; a nuclear war that could destroy the whole world. He turned the ships away to avoid further conflict and to avoid hot war.
On the 25th October, Kennedy took away the naval blockade/Cuban quarantine line. The next day Khrushchev sent a letter proposing to remove Soviet missiles from Cuba if the U.S. promised/guaranteed not to invade Cuba- this released some tension between the relations as they were making some fair decisions. But on October 27th an American U2 spy plane was shot down over Cuba and a second, more tough, letter from Khrushchev was received demanding the removal of U.S. missiles in Turkey. The U.S. however ignored the second letter and agreed with the first as they were initially planned to remove missiles from turkey in the first place, therefore they were losing nothing.
Kennedy agreed to remove all missiles set in Turkey on the border of the Soviet Union in exchange for Khrushchev removing all missiles in Cuba and on October 28th Khrushchev broadcasted an announcement on Russian Radio that, the Soviet government were dismantling the weapons and were returning them to the USSR. Kennedy immediately responded with a statement, saying that her wanted peace between the two governments and that he will not interfere with cuban affairs and not intrude on their land.
Khrushchev appeared to be weak and a laughing stock amongst communist politicians as, the removing of missiles from Turkey, were not made public at the time (secret deal between Kennedy and Khrushchev.) It appeared as though Kennedy had won conflict as Khrushchev had been humiliated; the Russians were seen as retreating from circumstances that they had started. Two years later Khrushchev lost his power.
This Crisis lead to the creation of the Moscow-to-Washington hot line, a telephone/communication link between Moscow and Washington D.C. Its purpose was so that the leaders of the two countries can communicate directly, efficiently and quickly in the case of another crisis. It is helpful and better to help solve such a crisis.