László Rajk (March 8, 1909 – October 15, 1949) was a Hungarian Communist politician, who served as Minister of Interior and Minister of Foreign Affairs. He was an important organizer of the Hungarian Communists' power (for example, organized the State Protection Authority (ÁVH)), but he eventually fell victim to Rákosi's show trials, probably, apart from the Communist parties' endemic power struggles, because he was a homegrown Communist, as opposed to the Stalin-backed Matyas Rákosi.
The Rajk trial marked the beginning of the anti-Titoist drive movement of Joseph Stalin. His trial also marked the beginning of the removal of all political parties in Hungary. The purges, however, left the economy in a truly disastrous state whereby a lack of capital inflow doomed the building projects that were underway. Also, a vast number of the intelligentsia were then employed on the sort of manual labouring duties usually reserved for skilled professionals. The result left the country with an inadequate infrastructure and unsatisfactorily manufactured goods. The government was also using too many men to search for spies within the country and not enough to perform the productive work to sustain the economy.
Dissatisfaction with Rákosi's rule began to surface and, on 28 March 1956, after a number of vast demonstrations, Rajk was rehabilitated. The rehabilitation speech, even though it was not publicized, had vast consequences for Rákosi, who had used the Rajk guilt as an explanation for the other purges that followed. Now that he had to admit that he was, indeed, wrong, it would end up ruining Rákosi's rightful authority.
The people then began to speak out against Rákosi, saying that he had lost their trust. Lászlo Rajk was then reburied, before 100,000 mourners, on October 6, 1956, along with two other men who lost their lives during the purges. (This was a precursor to the Hungarian Revolution of 1956, which began on 23 October.)
The only lingering question from the Rajk trial was who was to be held responsible for the activities for the late 1940s and early 1950s. Many victims have yet to have been identified following the purges, including those who lost their government positions merely because they were thought to pose a threat to Rákosi's reign of power.
More information on the English and Hungarian Wikipedia pages.