How did the dispute arise between the big-endians and the little-endians?

The terms big-endian/little-endian come from Jonathan Swift's Gulliver's Travels. In Lilliput, a royal edict required its citizens to open soft boiled eggs from the small end. In the rival kingdom of Blefuscu, they opened them from the big end, earning them the name Big-endians.

In computing, the terms are intended to indicate from which end a multi-byte numeric value is written. With little-endian, the least-significant byte always comes first (thus the value is written in reverse). This makes it much easier to cast from one type to another. For instance, a wide character consumes two bytes (a Word). For characters within the ASCII character set, the first byte is always 0x00 while the second byte stores the actual ASCII character code (0x00 to 0xFF). With big-endian notation, casting a wide character to an ASCII character results in the ASCII character always having the value 0x00 because that is the first byte. In little-endian, the bytes are reversed thus the first byte is the ASCII character code.