Kulak is a word that means "fist" in Russian, and was theoretically used to describe rich peasants in the countryside of the Soviet Union; the "fist" was of course the fist with which they supposedly oppressed the poorer peasants.
But in reality, the word ended up getting applied to any peasant which the Soviet regime took a dislike to. The Communists were almost all workers from the cities who had little understanding of rural areas - after the Russian Revolution, the people of the cities had to effectively re-conquer the entire countryside, which had escaped into self-rule; this is the event we know as the Russian Civil War. The gap of understanding was so large that after the Bolsheviks changed their name to the "Communist Party", many peasants declared themselves for the Bolsheviks and against the Communists; they had no idea they were referring to the same entity.
This split between countryside and town was problematic for the towns because all the food came from the countryside, and the Communists were worried that the peasants would effectively be able to starve them out. So, they launched an aggressive attempt to impose their control on the countryside by the program of collectivization, which essentially meant tearing up everyone's land deeds and reorganizing the peasants into huge, controllable farms. These farms weren't very efficient, but they were much easier to understand for the Soviets than the social structure of the traditional village, and easier to extract food from.
Anyone who opposed this attack on their way of life was branded a kulak and was shot as a "saboteur", because it was presumed only those under the influence of capitalism and the West could not desire what was good for the Soviet state, however catastrophic it was for themselves.