Animalism is the system of thought that Napoleon, Snowball, and Squealer make using the ideas that Old Major outlined in his speech in Chapter 1. Another way to say that is that it is the philosophy or ideology that the revolution will be based on. You can read about Animalism in Chapter 2.
By the time the three pigs have thought about it for a few months, they boil the ideas of Animalism down to the Seven Commandments that are listed in Chapter 2.
If you look at the Seven Commandments, you can see that the principles of Animalism revolve around the idea that animals are superior to people and that people are the enemy. You can see that animals are supposed to refrain from behaving in ways that would make them seem human.
Animalism is the belief that all animals are equals and that no animal is better or greater then the others around them
Animalism is a belif that animals are better than other human beings
Basically animalism is a doctrine or belief that man is purely animal, with no spiritual nature at all.