To really understand how Swift's exaggerations work as satire, you really have to know the political history behind the book. The links below will help set the stage for seeing how Swift uses colorful pictures to make strong statements.
Part of what makes Swift's satire work is how he shows how ridiculous people look when they argue over inconsequential things and ignore the things that are more important. For example, the Lilliputions choose their political leaders, not by elections based on issues, but on how well candidates dance on a rope. Both Brits in the 17th century and modern Americans can see just how silly it would look to have our politicians having a dance-off to determine who should be the next Representative. Making the Lilliputians only 6 inches tall just adds to the effect.
However, even while we laugh at the idea of dancing on a rope as a campaign tactic, how often do modern people vite based on how the candidate looks or how well he or she speaks instead of on the content of their platforms? It's this kind of satire that makes Gulliver's Travels as relevant today as it was in 1726.