In chapter 3, we see what happened after the death of Lenin as this story is mirroring how the results of the Russian Revolution fell into place through this allegorical story.
As Old Major represents Lenin or Karl Marx, after that leadership is gone, there is a vacuum of power. The pigs, thinking that they are the most intelligent (and they were), took control and begin processes of educating the other animals (indoctrinating the Russians), and training the young dogs from birth (creating a special military or police force). It is important to note which roles which pigs assume:
Napoleon - trains the dogs... privately.
Snowball - forms tons of committees and task forces.
Squealer - reports and makes excuses for why the pigs are beginning to have more privileges than others. The rest of the animals believe these lies.
They assume the role of leaders and lawmakers. Unfortunately, their version of a leader is not one who works alongside his "comrads" but rather someone who avoids labor by "supervising." This is the beginning of the pigs (leaders) taking special privileges for themselves while forcing all the other animals to be "equal." Of course, this eventually leads to the pigs eating better food, having bigger rations, residing in separate quarters, and avoiding hard, manual labor.
Orwell uses this assumption of power on the pigs' part to demonstrate how a totalitarian regime depends about the illusion that everyone is working equally hard for the good of the whole while in reality, the supervisors are the only ones gleaning from the sweat of the workers.
Taking their queue from the aging boar, Old Major, the pigs quickly take charge as the leaders in George Orwell's Animal Farm. However, the pigs do little work; they merely supervise the actions of the others. By this time, the pigs have taught themselves to read to better help them organize the daily operations of the farm. Snowball organizes committees and assists others in learning to read, while Napoleon turns his attentions to raising the youthful animals, including a litter of nine pups.
In this chapter, the pigs quickly assume the role of supervisors. They do not do any of the actual physical labor. Instead, they tell those who are doing the actual labor what to do. Orwell says that this was pretty much the natural thing to have happen. That is because the pigs were naturally more intelligent than any of the other animals.
In a way, the pigs are setting themselves above the other animals. As you go along in the book, this trend will intensify and the pigs will take more and more privileges for themselves.