Intro to the Hierarchical Liturgy
The Hierarchical Divine Liturgy is served whenever the bishop is present. Since the bishop is the shepherd of his church, he should preside at all his church’s celebrations, and that’s exactly what he did in the early church when the Christian community was small. In cathedrals, especially the Cathedral of Holy Wisdom (Hagia Sophia, our mother church where our liturgy developed), the presidency of a bishop was normative. When the bishop is present, the entirety of the Church is present.
The bishop is also called the hierarch or eparch as he is the ruling hierarch of an eparchy, i.e. an area over which he is pastorally responsible (AKA a diocese in the Latin Church). Today’s eparchy can easily span thousands of people and of miles, and sometimes tens of thousands of each. It is impractical to expect today’s bishop to be physically present at every service held in the eparchy. The bishop usually visits on special occasions in the parish such as ordinations, a big parish anniversary, or the parish Praznyk or patronal feast day. But, from a theological and liturgical viewpoint, the Hierarchical Divine Liturgy is actually the basic and normal Divine Liturgy of the Church. Technically, it is only by exception that any Divine Liturgy is served without the eparch.
The bishop is present at each service by means of various symbols which remind us of our unity with the bishop, and through him with the entire church, local and universal. For example, any celebration of Liturgy requires an antimins, which is a small cloth icon of Christ’s burial which was signed by the bishop and given to a particular priest for use in a particular parish or ministry, representing the bishop’s presence and thus the authorization of the entire Christian community to celebrate the Mysteries in that place.
The eparch represents in his office the Christian community (both laity and clergy) geographically in the local and particular Church. By his apostolic succession, he also makes present the Church historical, stretching back to the apostles. And by his communion with the patriarch, the college of bishops and all those with whom the patriarch is in communion, e.g. the other patriarchs and the first patriarch, the bishop and pope of elder Rome, the Eparch makes present the entirety of the Catholic communion.
You may notice that every so often during the Hierarchical Services, the language will suddenly change into Greek: eis polla Eti, Dhespota… Ton Dhespotin… Agios o Theos…. As the Rus’ (around present-day Ukraine) was evangelized by Byzantine missionaries, the first bishops and metropolitans of our Church were Greeks. By the work of Saints Cyril and Methodios, Equal to the Apostles and Teachers of the Slavic Nations, the Holy Scriptures and liturgical texts were translated into the local vernacular. Nevertheless, in gratitude to their missionary bishops who had to leave their homeland to minister to our Church and in remembrance of our connections with our mother Church, certain portions of the service are taken in Greek.
Letter to the Church of Smyrna by Saint Ignatius,
Patriarch of Antioch and Successor of Peter:

8:1 Do ye all follow the bishop, as Jesus Christ doth the Father…
Let no one, apart from the bishop, do any of the things that appertain unto the church.
Let that eucharist alone be considered valid which is celebrated in the presence of the bishop, or of him to whom he shall have entrusted it.
8:2 Wherever the bishop appear, there let the multitude be; even as wherever Christ Jesus is, there is the Catholic Church. It is not lawful either to baptize, or to hold a love-feast without the consent of the bishop; but whatsoever he shall approve of, that also is well pleasing unto God, to the end that whatever is done may be safe and sure.