The first answer to this post thoroughly covered the allegorical connections in part I of Gulliver's Travels.
Swift goes on to write three more parts to Gulliver's Travels. Each part takes him to a different imaginary place. These journeys tend to have less specific correlations to Swift's contemporary world, representing instead more generalized ideas about the society Swift lived and worked in.
In part 2, he goes to a land of giants called Brobdingnagians. These people represent a much more equitable country than Swift's England. In this land, people share their food without fighting over it.
In part 3 he is taken aboard a flying island called Laputa. Laputa is populated by a group of ridiculous scientists who are so scatterbrained and preoccupied that they cannot keep a thought going to its conclusion. These scientists correlate to some of the excesses of the scientific community during the Enlightenment, when scientific activity increased in both positive and negative ways.
Finally, Gulliver travels to the land of the Houyhnhnms. Houyhnhnms are morally evolved horses who take Gulliver in. Unfortunately, there is another race living nearby called Yahoos, who are depraved and violent. The Houyhnhnms represent moral righteousness; the Yahoos represent the worst of humanity. When the Houyhnhnms decide that Gulliver too closely resembles a Yahoo, they expel him from their country. When he returns home for the last time, he can no longer tolerate the company of humans, even his own family, whom he associates with the Yahoos.
Gulliver's Travels is a parody of the travel journals famous during Swift's time. In the story, divided into four book, he satirizes everything from British government to science, politics, religion, and society's vanity in general.
An allegory is a story when a character or event in the story represents both itself in the literal sense and something else in the figurative sense. It could be actual people, events, ideas, or places that it represents.
In Book I of Gulliver's Travels, many places, people, and events represent actual things in Swift's time. For instance, Lilliput is England and Blefescu is France. The arguements and silliness of the Low Heels and High Heels represent political factions of the Whigs and Tories. The disagreement between the Big Enders and the Little Enders over which end of the egg is the proper end to break represents actual problems between the Protestants and Catholics at the time.
There are also definite correlations between particular characters in the Lilliput community with political figures in the British political system. These connections take a little work for us to figure out today, but to Swift's audiences, these would have been as obvious as the objects of editorial cartoons are to us. They would have been a source of much laughter.