What is the role of a bishop?
Hierarchy of the Catholic Church
The typical role of a bishop is to provide pastoral governance for a diocese. Bishops who fulfill this function are known as diocesan ordinaries, because they have what canon law calls ordinary (i.e. not delegated) authority for a diocese. These bishops may be known as hierarchs in the Eastern Catholic Churches. Other bishops may be appointed to assist ordinaries (auxiliary bishops and coadjutor bishops) or to carry out a function in a broader field of service to the Church, such as appointments as papal nuncios or as officials in the Roman Curia.
Episcopal polity
An episcopal polity is a hierarchical form of church governance ("ecclesiastical polity") in which the chief local authorities are called bishops. (The word "bishop" derives, via the British Latin and Vulgar Latin term "*ebiscopus"/"*biscopus", from the Ancient Greek "epískopos" meaning "overseer".) It is the structure used by many of the major Christian Churches and denominations, such as the Roman Catholic, Eastern Orthodox, Oriental Orthodox, Church of the East, Anglican, and Lutheran churches or denominations, and other churches founded independently from these lineages.