The European Union(EU) includes countries and territories that are outside from Europe. For example, countries such as Aruba and Netherlands Antilles in the Caribbean are also part of EU though they are far away from mainland Europe and are closer to the US and North America than Europe. Similarly the beautiful island of Reunion in the middle of nowhere in the Indian Ocean is also in the EU since Reunion is a French overseas department.
The map below shows all the EU Overseas Countries, Territories and Outermost Regions:
Click to enlarge