The phrase "wet your whistle" means to have a drink, typically an alcoholic one. The origin of this phrase is somewhat debated, but here are the most commonly accepted theories: 

The phrase likely comes from the Old English usage of "whistle" as a slang term for the mouth or throat. Thus, to "wet your whistle" simply means to moisten your throat by drinking. 

Another theory is based on the idea that in the medieval period, some drinking mugs or tankards had whistles built into their handles. These whistles could be blown to signal for a refill. Thus, to "wet your whistle" would mean to take a drink and, by extension, to get a refill. 

An early recorded use of the phrase appears in a 14th-century song, suggesting that the phrase was used in a similar context even back then. The song goes: Whet your whistle with a drink, And think, how life may pass.