This is what you folks who are so dead set on atheism or who have an abject hatred for all organized religions have to really worry about when it comes to the Christian church. It means a movement toward unity and cooperation between all the various Christian religions. In other words, they'd all get together and gang up on you folks who are non-believers. Can you imagine it? A Mormon, a Jehovah's Witness, a snake handler and a Catholic schoolgirl all ring your doorbell at the same time, wanting to talk to you about Jesus (or his mother)?
The word comes from the Greek oikoumene, meaning "the inhabited world" and oikos meaning house. All of the world's people worshiping in the same house every Sunday? Roman Catholics used this word in the 1960's to refer to a concept of making Catholicism more responsive to other forms of Christian religions.
So far, the Roman Catholic, Orthodox, Pentecostal and Protestant churches have managed to agree on a few issues, such as baptism and the Eucharist, but you can bet your sweet holy water that these Protestants don't really find it comfortable to be in bed with the Catholics. In fact, when you hear the term evangelical, it is really a word that describes the movement away from ecumenism by some Protestants.
Likewise, some of the higher ups in the Catholic church today are not too happy with John Paul II's commitment to a greater folding in of all religions. See, this poor ol' dude is getting from the left (gay parades) and the right. Only a strong man can stand that heat.