Working EU can mean many different things:

1. You can be working in the EU. This means you work in one of the 27 countries of the European Union. Maybe you moved out of Ireland to find a job and settle in another EU country. In order to work in another EU country, you might need to speak another language or you might have been recruited because you were an English speaker. So you could be an Irish nurse working in Slovenia or an Irish IT expert working in Sweden.
2. You can be working for the EU, maybe in a European institution. Most of them are in Brussels, like the European Commission or the European Parliament. Some are in Luxembourg, like the European Court of Auditors. There are also tens of European agencies which are doted around the European Union. Their work is to focus on specific issues like medication approval, chemicals or banking. For example the European Food Safety Authority is in Parma, Italy.
3. You can be working on the EU. These jobs are largely concentrated in Brussels in think-tanks (bodies of experts that are providing advice and ideas) and public affairs companies, also known as lobbies. Lobbies’ work is to get European law-makers to take into consideration their problems. If your company works on environmental protection, you will try and influence the type of technology used in the car industry to make sure that future cars use as little fuel as possible.