The hierarchy (not to mention the terminology) of the Catholic Church can be rather complicated - especially if you did not grow up Catholic yourself. However, once examined, it can be seen that the organization of the Catholic faith is much like that of a military chain of command.
There is a single person in charge at the top - the Pope. The Pope has an advisory counsel, and then a series of patriarchs under him. Like the Pope, the patriarchs have their own counsels with a series of archbishops under them. This chain of advisory and subordinates extends all the way down to the priests who utilize their congregations to form their counsels.
Two specific terms will be described up front because of their definition as used in the Catholic Church is very different from their common usage:
The Pope
The Pope is the unquestionable and infallible head of the Catholic Church. He receives counsel from the Sacred College of Cardinals, but the Sacred College is not a legislative body - His Holiness, the Roman Pontiff retains complete control over the entire church.
Regardless of being The Pope, he is still just a bishop - technically the highest office in the church. However he holds the following jurisdictional titles, and because of these titles, he is above all other positions in the church.
In addition, he is given the following ecclesiastical titles:
Outside of his religious significance, he is also the Sovereign of the State of The Holy See/Vatican City/Vatican (a country) which makes him the equal of any other world leader or head of state.
Sacred College of Cardinals
As stated above, the Sacred College of Cardinals holds no true legislative power; however their position is that of a unique counseling body of the Pope. None of the cardinals in this college gain any new episcopal jurisdiction. They retain all of their previous responsibilities within the church - the position of cardinal simply adds to their original responsibilities. All cardinals are bishops (or archbishops).
While all cardinals are members of the Sacred College, there are separate groups within the College. These groups are listed in order of precedence:
Episcopal Cardinals
Episcopal cardinals are titular bishops in charge of the seven suburbicarian sees of Rome. Among the episcopal cardinals are the Dean and Subdean of the Sacred College of Cardinals who in effect are the second and third highest ranking bishops in the church. The seven titular cardinals include:
Presbyteral Cardinals
Below the Episcopal cardinals are the Presbyteral cardinals. They are all ordinaries, and many are metropolitans who have simply risen the ranks to the Cardinalate.
Diaconal Cardinals
The Diaconal cardinals were neither ordinaries nor bishops (though they are now - remember all cardinals are bishops), but were members of the Roman Curia or other cardinal deacons who were made cardinals and are appointed as titular archbishops.
The Roman Curia
Though technically not a part of the Catholic Church hierarchy, the Roman Curia is the governing body of the Holy See. Much of the work of the Pope is accomplished through the bureaucratic organization of the Curia which includes various councils, agencies, offices, and commissions just as any other country needs to have in place to make decisions and run smoothly. The Curia exists solely at the whim of the Pope.
The Episcopal Hierarchy
Patriarchs and Major Archbishops
Author's Note: The Patriarchs are one of the most confusing aspects of the Catholic Church (IMHO). Some references say there are only 12, while others state there are as many as 29 (or more). The names, titles, and locations of the patriarchs have changed numerous times over the years for various reasons including religious, political, and diplomatic.
Originally (325 AD), there were only three patriarchs of the church - the bishops of Alexandria (east), Antioch (east), and Rome (west). Over time, other bishops were named to the patriarchate. Basically, a patriarch is the "father" of a particular branch or sect of the Catholic Church that is traditionally centered on a geographic area (though obviously membership of each branch extends beyond the geographic area). Some of these branches include:
Primate
The title of Primate is honorary only, and is not used in the United States. A primate is the highest ranking bishop in a particular country. The primate holds no position of power among other bishops of his country - he is simply provided the respect of being the "first among equals" for his service.
Archbishops
Simply stated, an archbishop is the bishop of an archdioceses or ecclesiastical province (two or more dioceses). The archbishop of an archdioceses administers the archdioceses as well as his own diocese (he is, after all, still a bishop). The archbishop of a province is typically called a metropolitan, and reports directly to his patriarch (or to the Pope if he has no patriarch).
Bishops
Ordinary or Diocesan Bishop
In this case, ordinary does not refer to the bishop being a "plain old" bishop, but rather refers to his being a prelate who holds jurisdictional control over a geographical area. Ordinary bishops are in charge of a single diocese and report to their archbishop.
Auxiliary Bishops
While holding the title of bishop, the auxiliary bishop does not administer a diocese, but rather aids an ordinary bishop in the administration of his diocese.
Titular Bishops
A titular bishop is a bishop that is "in charge" of a titular see (i.e., the see no longer exists, or is in name only). It is primarily a title of honor, with a name taken from an ancient see from the Mediterranean or Holy Land. All auxiliary bishops are titular bishops, as are most bishops and archbishops who work in the Roman Curia.
Coadjutor Bishops
A coadjutor bishop is basically an ordinary bishop-in-waiting. The coadjutor holds their title cum iure successionis (with the Right of Succession). A bishop who is named the coadjutor bishop of a diocese will assume responsibility of a diocese upon the retirement or death of the current ordinary bishop. Because of this situation, coadjutor bishops are only appointed when another bishop is in poor health or nearing retirement.
Bishops Emeriti
Simply stated, a bishop emeriti is a retired bishop. Though retired, the emeritus bishop retains his bishopric title.
Diocesan Hierarchy
The bishop is the basic unit of the Catholic hierarchy; however under each ordinary bishop are numerous other administrative positions.
Diocesan Curia
Much like the Roman Curia under the Pope, the bishop employs the Diocesan Curia to help run his diocese.
Vicars General
The vicars general are the set of auxiliary bishops of the diocese plus a priest who govern with the bishop. The vicars are in charge of smaller geographic areas within the diocese (called a vicariate forane), each of these areas usually including multiple parishes (the actual church buildings). One of the pastors (or priests) of a parish in the vicariate forane is named the vicar forane.
Other Diocesan Offices
Other responsibilities within the diocese are the chancellor, vice-chancellor, and additional positions who record the decrees, dispositions, and other events of the diocese. Also included are a finance council, and a presbyteral council made up of local priests who advise the bishop.
Parishes
Each diocese is made up of multiple parishes which includes the physical structure of the church building and the community surrounding the building. A pastor (commonly called the Priest) is named the head of a parish, though for larger parishes there may be multiple priests. The head priest of any parish is called a parochial vicar.
In addition to the priest, Deacons are appointed to aid in the administration of the parish. Beyond this, the church is made up of its congregation. Members of the congregation can be appointed to various positions within the church to aid with daily or weekly activities. Some of these positions include finance and liturgy councils, lectors, acolytes, ushers, as well as a multitude of others.
Monsignors
Some priests are appointed by their bishop as monsignors (members of the monsignori). There are several classes of the monsignori including (in order of precedence):
See also