De-Stalinization started in 1956. It started in February of that year when Nikita Khrushchev, who was then leader of the Soviet Union, gave a speech in which he denounced the things that Stalin had done as leader. Khrushchev did this in part because he felt that the Soviet Union would be better off with policies that were farther from those of Stalin and partly because he wanted to weaken his political rivals, some of whom were still in favor of Stalin-type policies.
Khrushchev was able to do this in part because of a thaw in Cold War tensions. In 1955, the two superpowers had started to have somewhat friendlier relations. This was due in part to a split between China and the Soviets. This split influenced the Soviets to want better relations with the US. With an easing of tensions with the US, Khrushchev felt he could turn to domestic issues.