Four legs good, two legs bad.
This phrase is invented by Snowball - an intelligent, though a bit detached from reality, pig who shared the power with Napoleon and Squealer right after the Animal Revolution. The Seven Commandments given by Old Mayor were too long and too hard to understand for the majority of inhabitants of the Animal Farm (like the political mechanism is sometimes too complicated for the real-life people), so he created a quick fix.
Snowball lets the least intelligent animals like sheep learn this phrase by heart and take it as their motto. In some way he is right: the pigs had to build their government and spread the ideas fast, they didn’t have the time to teach everyone to read beforehand. This phrase protects the population of the farm from the outer enemy - the humans who oppressed them had two legs, they are bad, therefore not allowed to rule over the Animal Farm. But this simplification backfired spectacularly. The animals were perfectly protected from the enemy from outside, but when Snowball’s conflict with Napoleon reached the climactic point, he was proclaimed the inner enemy of the Farm.
The very existence of Snowball and his henchmen now allows Napoleon to change the Commandments, pretending that it is needed for the defense of the Farm. Snowball (who is long dead by that time), becomes an excuse to do anything. Moreover, when Napoleon sees that the minor changes of the Commandments go almost unnoticed and he is perfectly capable to shut up the rare ones who protest, he changes this very phrase too. Now it’s “Four legs good, two legs better” and the change is made when the pigs start walking on their two. Orwell uses this image to mock the leaders of the Communist party who nominally were equal to any other citizen, but they lived in luxury and had almost unlimited power to use and oppress the rest.