In many ways, the satire is a very simple one in this case. The Yahoos are meant to represent the general condition of the human race. As Gulliver comes to understand, these beings are so incredibly selfish and so driven to vice and disgusting behavior, that any time they gain an advantage or find a way to get more resources, etc., they immediately turn that windfall or that gain into a further journey into vice.
By contrast, he makes it clear that the Houyhnhms are so incredibly rational. So much of what they do makes great sense, etc. Of course Gulliver tries as hard as he can to make himself into the latter and avoid interaction with or implication that he is in fact the former.
This satirical treatment of the human race is only strengthened by later parts of the story when Gulliver returns home and voices his disgust with the behavior of the people he interacts with.
In Part 4, Gulliver finds himself in the land of the Houyhnhnms, who are intelligent and moral horses. He at first believes the horses are owned by humans, but then he realizes that the horses are their own masters. On the other hand, the Yahoos, who are human-like characters, live like animals and are nasty brutes.
This chapter satirizes humans' sense of moral superiority. For example, Gulliver's Houyhnhnm master says:
"I understand you well...it is now very plain, from all you have spoken, that whatever share of reason the Yahoos pretend to, the Houyhnhnms are your masters; I heartily wish our Yahoos would be so tractable."
The horse believes that even in Gulliver's European world, the horses are superior and that the humans, or Yahoos, only pretend to have reason (which they clearly lack).
In addition, the Houyhnhnms are so moral that they make humans seem like brutes. Gulliver states:
"And I remember, in frequent discourses with my master concerning the nature of manhood in other parts of the world, having occasion to talk of lying and false representation, it was with much difficulty that he comprehended what I meant, although he had otherwise a most acute judgment."
In other words, the Houyhnhnms don't even understand what lying and falsehood are. Their morality makes humans seem deceitful and inferior in contrast. While humans clearly believe in their own superiority, this section suggests that they are inferior. By extension, this part of Gulliver's Travels satirizes Europeans' notions of superiority and their sense that people in the rest of the world are brutes. Instead, Swift suggests that Europeans are brutes and that their sense of superiority is unfounded.