Borough \BUR-oh\ or \BUHR-oh\ , noun;
1. An incorporated municipality smaller than a city
2. One of the five administrative divisions of New York City
3. (In Alaska) an administrative division similar to a county in other states
1. An urban community incorporated by royal charter, similar to an incorporated city or municipality in the U.S.
2. A town, area, or constituency represented by a Member of Parliament
3. (formerly) A fortified town organized as and having some of the powers of an independent country
The origin of borough is Old English burg or burh ("a dwelling or dwellings within a fortified enclosure") which comes from Proto-Germanic *burgs ("hill fort, fortress"). Both ultimately derive from Proto-Indo-European *bhrgh, which meant "high" with derivatives referring to hills, hill forts and fortified elevations.
As Proto-Germanic split into German, English and others, the meaning of *burgs also split. In German and Old Norse it kept it's original sense, meaning "fortress, castle." In Gothic and English it became "town," which evolved into "incorporated town" in colonial America.
Pop Quiz: What does all this have to do with Canterbury, UK?
Answer: The place name ending -bury comes from byrig, which is the dative singular form of the Old English form of this word.