The church is government in itself, in fact if we will carefully study its organizational structure we can dare say that all of the management functions that we are using right now be it in government or private organizations has its basis in the church. The functions of Leadership, Supervision, Delegation, controlling, Planning and many other organizational principles traces its roots in the church.
The Pope being the Head of the church can be likened to a president of an independent nation. In fact the Vatican where the Pope resides is a Nation and he heads that nation. But unlike a president whose power and influence is confined to limited territory. The Popes sphere of power and influence is not limited in the Vatican. It extends worldwide. When there is a Roman Catholic Parish/Church there extends also the power of the Pope.
The Bishops somewhat functions like the Governors of a civil government because like the governors who heads a certain province or state. The Bishops also heads a certain territory/province or state and it is called Diocese.
The Diocesan Priest territory is called a Parish and the Parish council helps the Priest run the Parish. He is under the guidance and supervision of the Bishop of the diocese. The Parish Priest has similar functions like the Mayors of a City or Municipality.