The most likely explanation for this is that voters in the countries of the European Union do not care enough about their government to feel that there is any benefit to getting out and voting. This is likely due to the fact that the EU government does not have very clearly understood roles in people's lives.
People tend to turn out to vote when they feel that their vote can have an impact on their lives. This is not generally the case in EU elections. The EU government is a relatively opaque entity that is far away from the people and whose impact on the people is not completely clear. People do not understand very well the ways in which the EU government can affect their lives. Because of this, they do not think that EU elections are very important and they do not, therefore, turn out to vote.