Customs duty is a charge levied when goods are transported across a customs border. A distinction is made between import, transit, and export duties.
The European Union is a customs union, i.e. no customs duties are levied on transport and shipments within the EU area. By contrast, the import of goods from countries outside the EU is subject to customs duties. In such cases, import duties are levied by the Member States. The customs revenues are placed at the disposal of the EU.

Source: Wikipedia, edited (only available in German)