Any mixture of spirits and water, especially rum and water. The term comes from the nickname of ‘Old Grog’ for Admiral E. Vernon (1684-1757) of the Royal Navy who, in bad weather, habitually wore grogram (a coarse silk and mohair fabric) and who introduced the idea of serving diluted spirits to English sailors. Thus it invaded colonial customs and was known variously as Grog, Grogshop, Groggy, and Groggery (which was a that time also a term for low-class drinking places.)
Source(s): http://www.gaspee.com/ColonialRecipes.html