(Greek: oikoumene, the inhabited world)
Councils to which the bishops, and others entitled to vote, are convoked from the whole world under the presidency of the pope or his legates, and the decrees of which having received papal confirmation, are binding on all the members of the Church.
In normal times, when according to the Divine constitution of the Church, the pope rules in the fullness of his power, the function of councils is to support and strengthen his rule on occasion of extraordinary difficulty arising from heresies, schisms, relaxed discipline, or external foes.
It is the action of the pope that makes the councils recumenic.
When the pope has spoken ex cathedra to make his own the decisions of any council, regardless of the number of its members, nothing further can be wanted to make them binding on the whole Church.
New Catholic Dictionary