Question

What was the enemity between the kingdom of Lilliput and Blefuscu

Answer 1

In Gulliver's Travels, Gulliver discovers that Lilliput and a nearby island Blefescu have been at war for a long time over what seems to him to be a ridiculous issue: a dispute over which end one should break open when opening a hardboiled egg. The dispute over eggs extends back to the reign of the present Lilliputian emperor's grandfather, who, while a boy, cut his finger while attempting to break open his egg on the larger end. His father made a law against cracking eggs from that end, and it sparked a series of bitter civil wars that were encouraged by Blefescu: 

It is computed that eleven thousand persons have at several times suffered death rather than submit to break their eggs at the smaller end. Many hundred large volumes have been published upon this controversy; but the books of the Big-endians have been long forbidden, and the whole party rendered incapable by law of holding employments.

 

Gulliver's Travels is a satire, and Swift is using this absurd state of affairs to show that men go to war over things that aren't worth killing over. When understood in the context of his own time, he has in mind the series of conflicts between England and France that were intensified by the fact that England was a Protestant nation and France was Catholic, and that Catholic France had encouraged the pro-Catholic Stuarts during the seventeenth century, especially James II. If a giant from a faraway land had wandered into early eighteenth-century England, he would have probably viewed the conflicts between Britain and France as absurd as a long-standing war over eggs. I hope it helps you