Troika means "a group of three" or "triad" in Russian.
The first "operational troikas" (оперативная тройка) were introduced in the "centre", in the Moscow military okrug in 1929. The qualifier "operational" denotes they were based on the operational departments of the state police (OGPU). The troikas were tasked with administering quick punishment of anti-Soviet elements, without public trial or investigation. The sentences that were doled out, executions, were to be held in secret.
In January 1930, as part of the collectivization program, the Soviet Politburo authorized the state police to screen the peasant population of the entire Soviet Union. Normal legal procedures were suspended and the corresponding OGPU order of the 2nd of February, specified the measures needed for "the liquidation of the kulaks as a class". This instituted a regional based system for these troikas to work, so that the operations could be handed locally and with a quicker result. In each region, the troikas would decide the fate of the peasants branded as "kulaks". The troika, composed of a member of the state police, a local communist party secretary, and a state procurator, had the authority to issue rapid and severe verdicts (death or exile) without the right to appeal. In effect they served as judges, juries, and executioners.
The secret police troikas became an execution machine, implementing persecutions and torture of priests or other "anti-Soviet elements." This was done in secret and the victims of these trials often stood no chance at fighting the claims placed before them. They were often forced to give evidence against themselves and watch as the members of the troika sentenced them, often times to death.