Most animals in Animal Farm represent real people from the Russian Revolution and the USSR. Old Major, for example, is a combination of the founder of Marxism/communism, Karl Marx, and an integral member of the Russian Revolution and early leader of the USSR, Vladimir Lenin. Correspondingly, the boar's skull represents Lenin's embalmed corpse.
When Vladimir Lenin died in 1924, his body was preserved and placed in a mausoleum for thousands of Russians to visit. The Russian people begged for the body to remain on exhibition, and it has been to this day. We can assume that the body was preserved as a symbol of communism and to promote its principals, ultimately further enabling the Russian government's complete control over its people.
Similarly, Old Major, the father of Animalism and the instigator of the rebellion, was a symbol for the principals of Animalism. He motivates the animals to rebel when he stated, "Is it not crystal clear, comrades, that all the evils of this life of ours spring from the tyranny of human beings?" (11). Therefore, when he died, the pigs dug up his skull and kept it on display, marching the animals past it whenever they concluded a meeting. They used it as a sort of propaganda to control the animals and to keep them from questioning the pigs. After all, wasn't Animalism Old Major's idea?