(Photo: EU Commission)
Primacy means that which comes first.
EU law has primacy, and therefore prevails, over national law.
This principle was established in 1964 by the EU Court in the Costa-Enel case.
In 1970, the Court decided that EU law also prevails over national constitutions (Internationale Handelsgesellschaft case).

Primacy is also referred to as the principle of the superiority or supremacy of EU law and is analogous to the superiority of federal law over provincial or local state law in states like the USA, Canada, India, Germany, or Russia.

The future

This principle has been elplicitly inserted in Art. I 10 of the Draft Constitution.
The British government representative has criticised the wording with the argument that all powers come from the Member States and not from the new constitution.
There is a major potential conflict because no single Member State - except Ireland - has explicitly accepted the primacy of EU law over its own national constitution.
The Irish Constitution contains the principle of primacy of the EU law in its Art. 29.4.10.
France, Germany, Finland and Portugal mention the EU in their constitutions but do not accept primacy of EU law towards their constitutions.