The Brobdingnagians are giants: they average around 60 feet tall, and their lands and animals are correspondingly huge. Gulliver is incredibly vulnerable in this country, which is why it makes sense that the satire turns increasingly towards the fragility (and grotesqueness) of the human body. Gulliver stumbles into cow pats and is nearly drowned by a frog. All of these tales are truly dire to him, but to the Brobdingnagian court, they are a laugh riot.
In fact, Gulliver's own ego becomes a subject of satire in this section of the novel. The Brobdingnagian King asks Gulliver if he is a Whig or a Tory (about which, see our "Character Analysis" of the Lilliputians), and then laughs. The difference between Whigs and Tories matters about as much to a Brobdingnagian as the distinction between Lilliputian high and low heels matters to Gulliver. Brobdingnag gives Gulliver a taste of his own medicine. On the last island, he was fed and clothed by thousands of servants. Now, he receives the services of Glumdalclitch, a 9-year-old who treats him like a doll.
Once Gulliver has thoroughly learned the Brobdingnagian language, the King begins to ask him questions about how England is ruled: why is the state in debt? Why do people gamble? The King asks some probing questions about England that Gulliver can't answer (and that, presumably, the reader is supposed to mull over). He concludes that England is pretty lousy.
Gulliver tells the reader to forgive the King his ignorance about the true greatness of England (definitely some sarcasm going on here, considering the content of the Lilliputian satire). He adds the following story as proof of his foolishness: Gulliver offers the king a recipe for gunpowder. The King, hearing what gunpowder is for and what it can do, demands that Gulliver never mention it again, ever. The Brobdingnagians do have an army, because they occasionally fight civil wars, but that army is held in common as a peacekeeping force (kind of like the United Nations), and doesn't need a full-scale artillery or anything.
So, the Brobdingnagians are pretty great: fewer wars, clearer writing, straightforward laws, and so on. But they are still human – they still fight and seek profit. Their humanity becomes disgustingly, enormously apparent in Gulliver's descriptions of Brobdingnagian bodies. Because he can see them so magnified, he can see their moles sprouting giant hairs, their skin looking awful. Honestly, there's a description of a cancer in there that we simply can't bring ourselves to repeat.
Gulliver's revulsion focuses a lot on women: he sees the farmer's wife breast feeding, and thinks, "no object ever disgusted me so much as the sight of her monstrous breast" (2.1.6). He comments on the nipple, as large as his head, and the coarseness of her skin when seen so close. This total disgust with the sight of things that are supposed to excite Gulliver – breasts – foreshadows his final rejection of his wife and her smell after his stay in the country of the Houyhnhnms.