Such officers are found in hierarchically organised churches of Western Christianity which have an ecclesiastical legal system. For example, diocesan bishops are ordinaries in the Roman Catholic church and the Church of England. In Eastern Christianity, a corresponding officer is called a hierarch (from Greek ἱεράρχης hierarkhēs "president of sacred rites, high-priest" which comes in turn from τὰ ἱερά ta hiera, "the sacred rites" and ἄρχω arkhō, "I rule").
Within civic governance, notably in the southern United States, the role of the county ordinary historically involved the discharge of certain, often legal or legally related, tasks falling to city or county authorities, such as licensing marriages and adjudicating claims against an authority.
In canon law, the power to govern the church is divided into the power to make laws (legislative), enforce the laws (executive), and to judge based on the law (judicial). A person exercises power to govern either because the person holds an office to which the law grants governing power or because someone with governing power has delegated it to the person. Ordinary power is the former, while the latter is delegated power. The office with ordinary power could possess the governing power itself (proper ordinary power) or instead it could have the ordinary power of agency, the inherent power to exercise someone else's power (vicarious ordinary power).
The law vesting ordinary power could either be ecclesiastical law, i.e. the positive enactments that the church has established for itself, or divine law, i.e. the laws which the church believes were given to it by God. As an example of divinely instituted ordinaries, Catholics in communion with the Holy See believe that when Jesus established the Church, he also established the episcopate and the primacy of Peter, endowing the offices with power to govern the Church. Thus, in the Catholic Church, the office of successor of Simon Peter and the office of diocesan bishop possess their ordinary power even in the absence of positive enactments from the Church.
Many officers possess ordinary power but, due to their lack of ordinary executive power, are not called ordinaries. The best example of this phenomenon is the office of judicial vicar, a.k.a. officialis. The judicial vicar only has authority through his office to exercise the diocesan bishop's power to judge cases. Though the vicar has vicarious ordinary judicial power, he is not an ordinary because he lacks ordinary executive power. A vicar general, however, has authority through his office to exercise the diocesan bishop's executive power. He is therefore an ordinary because of this vicarious ordinary executive power.