"Supra" means "above" - in this case "above the nations".
As a member of the EU, a state gives up its sovereignty to the supra-national EU. Thus, a country can no longer decide various domestic and international policies on its own.
The EU voting systems can mean that if a majority of members in the EU adopt a law it will also come into force in countries that voted against it. In this way the national parliaments have transferred some of their powers (competence) to the EU institutions.
See also Primacy.