Animal Farm is largely an allegory for the Russian Revolution of 1917 and the subsequent evolution of the Soviet Union. It is not a part-for-part transcript, but the general timeline and major events are meant to be very similar. In the story, Old Major is an aged, prize-winning hog, who tells the other animals of his dreams about rebelling against the humans, who he identifies as being the source of all their problems.
Old Major is intended to represent two historical figures: Karl Marx and Vladimir Lenin. His name is, in a sense, part of the allegory; these two men are "major" figures in the history of communism and the Soviet Union. Both Marx and Lenin called for revolution, targeting capitalism as the source of misfortunes, and did not live to see these revolutions to completion (Lenin did survive the Russian Revolution but was crippled by strokes and essentially brain dead). Similar to Lenin, Old Major's body (or at least, his skull) was preserved and put on display, and the character and his ideas were venerated, elevated to a near-mythical status, and universally celebrated; indeed, it is difficult to argue against the truth of Old Major's speech, and difficult to criticize him personally because he never acts on it.
After Old Major dies, the cause of rebellion is taken up by two younger pigs, Napoleon and Snowball. At first the rivalry between these two is nonexistent - they are simply pigs/intelligentsia, heirs to Old Major's ideas and the best choices for interpreting and applying his ideas. The animals generally agree that rebellion and independence are attractive ideas, but the world that this rebellion will create is confusing and worrisome to them for various reasons; for example, Mollie is more concerned with ribbons and sugar than with practical concerns like food and defense. The pigs "get it" and are therefore able to coerce, as well as manipulate, the other animals into nurturing the rebellion until it actually takes place in Chapter 2.
After the death of old major, the idea of the rebellion takes on full force only to spiral down into havoc. When old major was alive the idea of the revolution was strong and when he died it gave that final push for the revolution (also the lack of care and food was another big push). But when the animals finally got their freedom, they were merely enslaved again by the pigs, under the belief that everything they were doing was to aid the lives of animals in order to make them better. In the end the animals turned a blind eye to how they were being abused by the higher power (the pigs) and by the end the revolution no longer stood for what it once stood for.