Basically, this uprising happened because the people of Hungary were unhappy with the communist government that was running their country. They were especially unhappy with the fact that the Soviet Union was basically telling their country what to do. They wanted more freedom for their country to act independently of the Soviet Union.
The Hungarians felt that they actually had a chance to get more freedom. This was because the USSR was going through a period of deStalinzation after Stalin's death. It appeared that the Russians were going to be more open and do less to try to control other countries.
The Hungarian rebels were really fairly unorganized militias. They rose up and started fighting against the government's forces. It might have had a chance of success except for the fact that the USSR decided to send its army into Hungary to crush the rebellion.
In the aftermath of the rebellion, the Soviet Union's power over all of Eastern Europe was no longer questioned--all communist countries would pretty much be forced to do what the USSR told them to do.
The Hungarian Uprising (also called the Hungarian Revolution) was the first popular uprising against the Soviets since their takeover of Eastern Europe after World War II. The uprising was in part inspired by the apparent liberalization of Soviet policy after Soviet leader Nikita Khrushchev attacked the leadership of former Soviet leader Joseph Stalin.
The uprising began on October 23 as a student demonstration in Budapest, during which students called for individual freedoms, a Hungary free of foreign control, a democratic socialist government, and Hungary's admission into the United Nations; after a student was shot to death by the state police (the ÁVH), the uprising swept the country. Local military groups then fought against the Soviets and the state police. The government collapsed, and the former leaders fled to the Soviet Union as Imre Nagy took over and petitioned the United Nations for support. However, the western powers did not want to become involved in battling against the Soviets and did not intervene. Fighting stopped until November 4, when Soviet troops entered the country and crushed the uprising, which ended on November 10. About 2,500 Hungarians and 700 Soviets were killed in the conflict, and many Hungarians fled the country in the aftermath of the revolution. In 1958, Nagy was executed for his role in the uprising. The government cracked down on dissidence with arrests following the revolution.