Noun
One of the chief administrative divisions or provinces of the Ottoman Empire; -- formerly called eyalet.
Source: Webster's dictionaryIn 1905, the city had 32,000 inhabitants, making it the largest of the vilayet, although closely followed by Prizren with its 30,000 inhabitants. Source: Internet
The British understanding was that "Damascus" meant the vilayet and not the city of Damascus, and accordingly virtually all of Palestine was excluded from Arab control. Source: Internet