An archdiocese exists because Roman provinces had capitals, and the bishop of a provincial capital, the metropolitan, came to hold real authority over the bishops of the smaller towns in the same province rather than merely a title of honour. The pattern was already assumed at the Council of Nicaea in 325, whose canons speak of a metropolitan confirming the election of a province's other bishops, and it hardened over the following centuries into a fixed rank: an archdiocese is the metropolitan's own see, and the neighbouring dioceses under its authority are called suffragan.
The system reached England directly from Rome rather than developing locally, when Pope Gregory the Great sent Augustine to Kent in 597 and made Canterbury the primatial see of the newly planted English church, a decision that still shapes the structure of the Church of England and, after the Reformation split it from Rome, of the Anglican Communion that grew out of it.
Eastern Christianity kept a parallel structure under different names, its patriarchates and metropolitanates tracking the old civil dioceses and provinces of the Byzantine east. The rank survived the political map that produced it by many centuries, so that an archbishop's authority over suffragan bishops today still echoes a Roman governor's authority over the smaller towns of his own province.