Squealer's role in Animal Farm is to disseminate propaganda which makes the animals accept whatever Napoleon tells them. To do this, he uses a number of propaganda techniques. Here are some examples.
Firstly, Squealer uses scapegoating. Whenever something goes wrong on the farm, you'll notice that he blames Snowball instead of admitting the truth. By doing this, he shifts blame and responsibility from Napoleon, thereby increasing Napoleon's prestige.
Secondly, Squealer also uses false science. When he justifies the pigs' theft of the milk and apples, for example, Squealer claims that it is scientifically proven that pigs need to eat milk and apples because they are good for the brain. The animals do not question the arguments of scientists, thereby enabling the pigs to continue their theft.
Thirdly, he also uses distraction techniques. Notice how whenever Squealer is justifying something that Napoleon has done, he is always moving around. When he is denying that Boxer has gone to the "knacker's," for example, Squealer is described as skipping from side to side and whisking his tail. By doing this, he ensures that the animals are not focusing on his words, but are instead focusing on his movements.