Shared competence
"A shared competence" would normally entail that two different decision-makers share the right to decide and make laws.
When the EU and its member states share a competence, the member state loses its 'competence' (power to take decisions) when the EU decides to regulate. So EU legislation does not only replace the content of a national law, it also removes the national right to legislate.
The future
The EU Constitution proposes in Art. I-13 that the following areas become shared competences: competition rules within the Internal market; the Area of Freedom, Security and Justice; Agriculture and Fisheries; Transport; Trans-European networks; Energy; Social and Employment Policy; Economic; Social and Territorial Cohesion; the Environment; Public Health; and Consumer Protection.Links
See also Categories of competence and Convention working group on Complementary Competence.