The European Union or EU is a collection of European countries which have formed a social and economic union. This has had important consequences for teachers there.
Essentially citizens of any EU country have the right to live and work in any other EU country and they will receive preferential treatment when it comes to finding work. Notably the bureaucracy involved is much simpler than for non-EU citizens when it comes to visas and work permits, freedom of movement and suchlike. In other words, citizens of non-EU countries such as the USA and Canada will find it hard to secure work within the EU unless they are especially well qualified and experienced.
Note, for more about finding work in the EU (especially for non-EU citizens) see this article: Teaching in the EU for Non-Europeans.
The following countries are members of the EU:
In addition there are a number of countries who are candidates for joining the EU in the near future. This means that in they will soon need to change their laws to come into line with EU directives. Non-EU citizens who are currently working in these countries may well find that once the country does join the EU they may lose their jobs.
A number of other countries bordering the EU are making moves to join.
Europa - official website of the EU