In the Tsarist system, there was an upper class of aristocracy that controlled the country and had a standard of living much higher than the general population. Then there was a revolution that overthrew that system, and then the revolution was hijacked by the Bolsheviks, who claimed to be taking the country over on behalf of the people to destroy the class system and institute an egalitarian society.
However, the Communist Party became the new ruling class, with the upper echelons enjoying a standard of living much higher than the general population. So while they destroyed the old system of Tsarist aristocracy exploiting the working class, they replaced it with a system that also exploited the working class, just with a different set of people doing the exploiting.
The humans in animal farm represent the capitalists/bourgeoisie/aristocracy. The pigs represent the Communists in general and the Bolsheviks, especially the upper echelons, in particular (the dogs also represent Bolsheviks, but enforcement arms such as NKVD rather than the ruling elite).
The pigs took on much of the attributes of the humans (wearing clothes, walking on two legs, etc.) and began exploiting and oppressing the rest of the animals, just as the humans did. The pigs have taken on the role of the humans, and the farm is run much as it was before the revolution, except with different people running it. This parallels how the USSR and Tsarist Russia were run by different sets of people, but the USSR was just as exploitive and oppressive, and the main difference between the two was just who was ruling, and not how they ruled.
