Wikipedia: http://en.wikipedia.org/wiki/High-_and_low-context_cultures

Short version, in a 'high context culture', things can be left unsaid and the cultural background will explain effectively to people within that culture (and less effectively to people outside that culture).

A Texan (the American south is high context) can say quite a bit with 'yep...' and letting the culture explain the rest of the meaning.

In a low context culture, less emphasis is placed on single word choices (though they can still be important) and more explanation of the entire context of the communication is done.