In the Nicene Creed, we say that we "believe in one holy catholic and apostolic church." The word "catholic" comes from the Greek katholikos, which means "universal".
When we say "catholic", we are referring to the church throughout all time, not just a specific denomination. The Roman Catholic Church is just that, the branch of the universal church out of Rome.
The word "catholic" also expresses not only our shared origin as a church, but the hope that one day we may all be one. That is why the ecumenical movement is so important. The Anglican Communion as a whole has been in talks with both the Roman Catholic Church and the various Orthodox Churches in order to come together through our common ground in Jesus Christ. In The Episcopal Church, we have made the journey to be in full communion with other denominations, including the Evangelical Lutheran Church of America. There are many other denominations we continue to be in talks with, and the hope is that those conversations will be fruitful as well.