So what exactly is European Federalism you ask?
Well the really short version is support for the development of the European union into a "ever deeper and wider union" as codified in the new European Union constitution.
Of course this is a gross oversimplification, and depending on who you ask there are as many answers as there are people. But hey the one good thing about Europe is that we certainly are diverse, even in our opinions.
The long version would take more time to write than I currently have so it will have to wait for a later date.
So to what extent is the European Union a federal entity at this time?
The European Union operates by the way of competencies ,which are basically areas where the member countries have conferred authority to the EU so that all decisions on that particular issue are decided exclusively at the EU level.
These competencies include the common market, Eurozone monetary policy, common commercial policy, customs union and conservation of marine biological resources
So is European Federalism synonymous with with wanting to form a "United States of Europe?"
Not really, the European Union is not really comparable to any other entity such as the United States or Russia (which is after all a federation). Rather think of the EU as a Sui Generis entity, that's Latin for "entity unlike anything else."
This term stems mostly from the fact that the EU has many trappings of statehood, such as a constitution, a parliament, a president, and a supreme court, these legislative and judicial bodies are however very limited in scope by the European constitution.
And here it gets interesting, the European constitution is not really a constitution per se but rather a treaty that rigidly defines the responsibilities and competencies of the Union, as contrasted to the United States Constitution that makes general statements that are then interpreted by the supreme court.
This is the main reason why the European constitution weighs in at a hefty 60,000 words compared to the US constitution with 4,600 words.
So as we can see while the EU may resemble a federation the truth is somewhat different.