The European Union consists of...

The European Parliament
The Council of the European Union
The European Commission
The Court of Justice
The Court of Auditors
The European Economic and Social Committee
The Committee of the Regions
The European Central Bank
The European Investment Bank

The goals of the European Union are "Peace, prosperity and freedom for its 495 million citizens — in a fairer, safer world."

Results so far:
Peace - safer food, environmental issues are discussed
Prosperity - poorer regions have higher living standard, cheaper air travel
Freedom - free travel and trade, the Euro as single European currency

... and much more!

The most important bodies to make these things happen are:

The European Parliament (representing people) - established 1952 (as Common Assembly), meets in Strasbourg, France, and Brussels, Belgium
The Council of the European Union (representing national governments) - established 1952, meets in Brussels, Belgium
The European Commission (representing common interest) - meets in Brussels, Belgium