From the longer English Wikipedia page 
Nikita Sergeyevich Khrushchev (April 15 [O.S. April 3] 1894 – September 11, 1971) was a politician who led the Soviet Union during part of the Cold War. He served as First Secretary of the Communist Party of the Soviet Union from 1953 to 1964, and as Chairman of the Council of Ministers, or Premier, from 1958 to 1964. Khrushchev was responsible for the de-Stalinization of the Soviet Union, for backing the progress of the early Soviet space program, and for several relatively liberal reforms in areas of domestic policy. Khrushchev's party colleagues removed him from power in 1964, replacing him with Leonid Brezhnev as First Secretary and Alexei Kosygin as Premier.
The Secret Speech, while it did not fundamentally change Soviet society, had wide-ranging effects. The speech was a factor in unrest in Poland and revolution in Hungary later in 1956, and Stalin defenders led four days of rioting in his native Georgia in June, calling for Khrushchev to resign and Molotov to take over.
The Secret Speech, combined with the death of Polish communist leader Boleslaw Bierut, who suffered a heart attack while reading the Speech, sparked considerable liberalization in Poland and Hungary. In Poland, a worker's strike in Poznań developed into disturbances which left more than 50 dead in October 1956. When Moscow blamed the disturbances on Western agitators, Polish leaders ignored the claim, and instead made concessions to the workers. With anti-Soviet displays becoming more common in Poland, and crucial Polish leadership elections upcoming, Khrushchev and other Presidium members flew to Warsaw. While the Soviets were refused entry to the Polish Central Committee plenum where the election was taking place, they met with the Polish Presidium. The Soviets agreed to allow the new Polish leadership to take office, on the assurance there would be no change to the Soviet-Polish relationship.
The Polish settlement emboldened the Hungarians, who decided that Moscow could be defied. A mass demonstration in Budapest on October 23 turned into a popular uprising. In response to the uprising, Hungarian Party leaders installed reformist Premier Imre Nagy. Soviet forces in the city clashed with Hungarians and even fired on demonstrators, with hundreds of both Hungarians and Soviets killed. Nagy called for a cease-fire and a withdrawal of Soviet troops, which a Khrushchev-led majority in the Presidium decided to obey, choosing to give the new Hungarian government a chance. Khrushchev assumed that if Moscow announced liberalization in how it dealt with its allies, Nagy would adhere to the alliance with the Soviet Union. However, on October 30 Nagy announced multiparty elections, and the next morning that Hungary would leave the Warsaw Pact. On November 3, two members of the Nagy government appeared in Ukraine as the self-proclaimed heads of a provisional government and demanded Soviet intervention, which was forthcoming. The next day, Soviet troops crushed the Hungarian uprising, with a death toll of 4,000 Hungarians and several hundred Soviet troops. Nagy was arrested, and was later executed. Despite the international outrage over the intervention, Khrushchev defended his actions for the rest of his life. Damage to Soviet foreign relations was severe, and would have been greater were it not for the fortuitous timing of the Suez crisis, which distracted world attention.
In the aftermath of these crises, Khrushchev made the statement for which he became well-remembered, "We will bury you" (in Russian, "Мы вас похороним!" (My vas pokhoronim!)). While many in the West took this statement as a literal threat, Khrushchev made the statement in a speech on peaceful coexistence with the West. When questioned about the statement during his 1959 U.S. visit, Khrushchev stated that he was not referring to a literal burial, but that, through inexorable historical development, communism would replace capitalism and "bury" it.
The Russian Wikipedia page is .
There is much other coverage - eg  on the Secret Speech.