One of the most significant ways in which Squealer ensures that the animals do not rebel against Napoleon is his constant justification of why things are good and his constant raising the spectre of Jones in explaining how things could be worse. Napoleon employs Squealer, already seen as a "brilliant talker," to dispense the "spin" amongst the other animals. Squealer is able to use statistics that sound very good to justify Napoleon's rule. At the same time, he is able to tap into the fundamental fear, or at least perceived fear, of Jones' return. Squealer is able to clearly identify that the most basic fear of all of the animals is Jones' return. In this light, Jones is seen and depicted as the worst evil. This is significant as Squealer makes the arguments to the animals that even if things are bad now, under an Animalist rule, life is better than under Jones, where the figure of the human controlling animals is the embodiment of exploitation and abuse. In being able to convince the animals that Jones, himself, is the ultimate representation of evil, the other animals put aside any voices of dissent. As long as the reality of there being something potentially worse, Squealer has a foothold into the mindset of the other animals. Squealer is able to convince them that life would be worse under Jones, silencing them into submission.
You may or may not be aware that Animal Farm is a satire regarding the Russian Revolution, and following communist doctrine under Stalin. In this comparison, Squealer is representative of communist propaganda. Orwell sets this comparison up when he first introduces Squealer at the beginning of Chapter 2. "He was a brilliant talker, and when he was arguing some difficult point he had a way of skipping from side to side and whisking his tail which was somehow very persuasiv.The others said of Squealer that he could turn black into white."
At any point in the novel where the rest of animals begin to question the world order Squealer uses this technique, of twisting the truth, to sway them once more into obedience. An example of this is at the end of Chapter 3, when the animals question why the pigs receive all the apples and milk. Squealer is sent to make explanations to the others.
Squealer prevents the animals from rebelling against Napoleon by clever use of his words, and his ability to twist the truth and manipulate the animals.