John Allen describes all the goings-on here. Check out what the central activity of the world's oldest Christian church looks like.
I think that Allen's summary is useful from an apologetics perspective since it can inform the imagination of people who are so accustomed to thinking of the Christian churches only at the local level. To see how the Pope, cardinals, and bishops administer the unity and mission of the church at "headquarters" can help break us out of that box. Of course, the church at the local level is (or at least ought to be) integrated in union with the bishops and the Holy Father, since we all share the same mission of the Redeemer, and we all share a place in the same episcopal hierarchy (though not necessarily the same place).