(plural cups of joe)
- (chiefly US, idiomatic) A cup of coffee.
The possible source is as a shortened form of 'a cup of jamoke' - which was a common reference to coffee, its being a compound of Java and Mocha. There are examples of the jamoke usage throughout popular culture including in the Preston Sturges movie Hail The Conquering Hero (1944).
An alternative, plausible theory is that since "joe" is a term for a "fellow, guy, or chap," a cup of joe is referring to the common man's drink. The use of joe in the earlier reference can be traced back to 1846.
One popular but erroneous attribution is to Josephus Daniels (1862-1948) who, as Secretary of the U.S. Navy under President Woodrow Wilson in 1913, was said to have abolished the officers' wine mess. And thus coffee became the strongest drink aboard navy ships known as "a cup of Joe".
For more see: http://www.snopes.com/language/eponyms/cupofjoe.asp