When you hear of companies like Apple having their money offshore, you might imagine piles of gold bullion or paper bills sitting in a physical bank somewhere in Switzerland or Ireland. More likely that money is residing in one of the big banks head-quartered somewhere in the United States. (For that matter, it is likely residing as so many numbers in a computer run by one of these banks and not piles of paper or gold.)
The Times and Slate explain it here: For U.S. Companies, Money ‘Offshore’ Means Manhattan – The New York Times and Offshore accounts not actually offshore.