From the AP article:
The European Union expanded at midnight Friday to take in a region isolated during the Cold War, creating a 25-nation economic giant with the potential to rival the United States. Church bells rang and fireworks exploded over eastern Europe in celebration.
What does this mean for Europe? A lot. The inclusion of Eastern Europe in the European Union (instead of part of a Greater Russia) means that these smaller countries are now an integral part of Europe. Not only does this prevent Russia from having a sphere of influence in Eastern Europe (which was an integral part of the supposedly "European" heritage of Russia - again, props to our boy Peter), it heralds the successful adoption of "Western European" values of liberal democracy in the "new" Europe.
While the first paragraph (excerpted above) seems to imply that the new European Union will rival the United States in global hegemony, I doubt that this will be the case. If anything, I think the EU will serve as a more humanistic ally of the United States. Regardless of what their governments might think, the populations of the various European countries have shown themselves to be more dedicated to human rights that their American counterparts.