The European Union is a unique economic and political union between 28 European countries that together cover much of the continent. The EU was created in the aftermath of the Second World War. The first steps were to foster economic cooperation: the idea being that countries that trade with one another become economically interdependent and so more likely to avoid conflict. The result was the European Economic Community (EEC), created in 1958, and initially increasing economic cooperation between six countries: Belgium, Germany, France, Italy, Luxembourg and the Netherlands. Since then, a huge single market has been created and continues to develop towards its full potential. 
The EU is an organisation within Europe. It is not a reference to the continent itself.
At the moment, the UK is debating whether to leave the EU.