Orwell portrays conflict on multiple levels. At the beginning of the book, Old Major's speech details the conflict between the animals and their human masters, particularly Jones. After detailing the misery and oppression the animals face, he traces their origin to the people that use them:
There, comrades, is the answer to all our problems. It is summed up in a single word — Man. Man is the only real enemy we have. Remove Man from the scene, and the root cause of hunger and overwork is abolished for ever.
Once man is overthrown, another conflict emerges. This time, it is the farm against the rest of the English countryside. The pigs, in the interest of maintaining their power, play up this conflict, suggesting (initially with some justification) that the humans outside the farm are in league against them. The humans do, indeed, attack the farm on two different occasions, resulting in the Battle of the Cowshed and the destruction of the windmill. Eventually, though, the pigs form an alliance with the humans, even as they continue to persuade the animals that Snowball is scheming to destroy the farm.
Another, less tangible conflict is that between appearance and reality. Throughout the book, the pigs manipulate reality to justify Napoleon's rule. For example, Squealer, the propagandist, persuades the skeptical animals that Snowball had actually led the humans against the animals at the Battle of the Cowshed. This conflict is played out in written form on the side of the barn, where the Seven Commandments are gradually winnowed down to one:
ALL ANIMALS ARE EQUAL BUT SOME ANIMALS ARE MORE EQUAL THAN OTHERS.
The animals can never remember exactly what has changed when they read the commandments, suggesting that in many ways, appearance, in the form of propaganda, wins out, as the following example from the aftermath of Napoleon's purges demonstrates:
A few days later, when the terror caused by the executions had died down, some of the animals remembered — or thought they remembered — that the Sixth Commandment decreed “No animal shall kill any other animal.” Muriel read the Commandment for her [Clover]. It ran: “No animal shall kill any other animal WITHOUT CAUSE.” Somehow or other, the last two words had slipped out of the animals’ memory...