From the game's encyclopedia
An Archdiocese is the Christian form of a Clerical Region, an ecclesiastical domain held by an Archbishop through its Clerical Title and seated in a capital County, where a Grand Cathedral may be raised.
A Christian Ruler answers in spiritual matters to the Archbishop of the Archdiocese that contains their Capital County, and the territory subject to Archdioceses collectively constitutes The Christian Church Situation.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Archdiocese is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "An Archdiocese is the Christian form of a Clerical Region, an ecclesiastical domain held by an Archbishop through its Clerical Title and seated in a capital County, where a Grand Cathedral may be raised." It is part of Faith. The game also links it as Archdioceses. Patch 1.20.1.2, from game/common/game_concepts/pam_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/pam_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.