At its heart, Animal Farm is a warning against the dangers of totalitarianism. Specifically, Orwell argues that after a revolution, the people should not allow power to be concentrated into the hands of a single individual or small group of individuals because if this happens, that power will corrupt the leaders and turn them into self-interested tyrants.
Orwell supports this argument through the characters of the pigs, particularly Napoleon, who become increasingly greedy and self-interested as the story progresses. Moreover, they corrupt the ideas of Animalism, the foundation for their new society, and, by the end of the novel, have become just as tyrannical as the humans they overthrew. More importantly, by the time the other animals realize what has happened, it is too late. They are trapped in a dictatorship, unable to change their situation.
In terms of allusions, this argument also applies to the political situation in the Soviet Union. Through his allusions to Soviet leaders, particularly Stalin, Orwell shows that this exact thing happened: Stalin corrupted the principles of communism and turned it into totalitarianism.