The terms Big-Endian and Little-Endian are from the Lilliput episode of Gulliver's Travels, where they are satires on the Protestant and Roman Catholic religions, and their effect as factions in the politics of the two rival and warring empires of Lilliput and Blefuscu, representing respectively Great Britain and France.
They refer to which end of the egg you crack open to eat. Reldresal, principal secretary to the Lilliputian emperor, explained it to Gulliver thus.
It began upon the following occasion. It is allowed on all hands, that the primitive way of breaking eggs, before we eat them, was upon the larger end; but his present majesty's grandfather, while he was a boy, going to eat an egg, and breaking it according to the ancient practice, happened to cut one of his fingers. Whereupon the emperor his father published an edict, commanding all his subjects, upon great penalties, to break the smaller end of their eggs. The people so highly resented this law, that our histories tell us, there have been six rebellions raised on that account; wherein one emperor lost his life, and another his crown. These civil commotions were constantly fomented by the monarchs of Blefuscu; and when they were quelled, the exiles always fled for refuge to that empire. 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. During the course of these troubles, the emperors of Blefuscu did frequently expostulate by their ambassadors, accusing us of making a schism in religion, by offending against a fundamental doctrine of our great prophet Lustrog, in the fifty-fourth chapter of the Blundecral (which is their Alcoran). This, however, is thought to be a mere strain upon the text; for the words are these: 'that all true believers break their eggs at the convenient end.'
By the time Gulliver arrives there are so many Big-endian exiles in the court of Blefuscu that that nation is launching a major assault on Lilliput, where Gulliver is now a free person. In gratitude for his freedom, he destroys the Blefuscudian fleet.