What kind of power does the European Union have?

The EU has power over the entire European Continent. They deal with things like economics. One example is the Euro becoming the main currency for the entire continent.

The European Union is a political and (more importantly) economic union of 27 sovereign states. It's main powers are connected with such things as single market and customs union, free movement of persons, goods, services and capital, competition rules, trade and commercial policy, borderless travel (Schengen area), monetary policy and single currency - the euro, consumer protection, transport, energy, medicinal products, food and medical devices, scientific research, agriculture, regional development, fisheries, protection of the environment and certain aspects of social policy etc. The EU takes some supportive actions in the areas of education, tourism and culture (in addition to actions of member-states). The EU also has a so called "common foreign and security policy" (relatively limited at the moment). Within the framework of the common security policy the EU can engage in common peacekeeping and anti-terrorist missions in different crisis areas.

More detailed information here: http://europa.eu/pol/index_en.htm