Game concept
Player Heir
From the game's encyclopedia
The Player Heir is the Heir that a player will keep playing as on Succession.
The Player Heir is usually the same as the Primary Heir, but if the Succession Law of your Primary Title dictates that it should go to a character outside of your Dynasty, you will instead keep playing as the dynastic heir to your second highest-tier title (or third, fourth, etc.).
This situation is common when your Player Heir is voted out under an Elective Succession Law. If you are House Head of a Noble Family in an Administrative Realm you may lose your Realm to Primary Heirs outside of your House but retain your Noble Family Title.
If you are Ecclesiastical, your Player Heir is the character who is set to inherit your Primary Title, usually an Archdiocese.
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.
Player Heir is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "The Player Heir is the Heir that a player will keep playing as on Succession." It is part of Heir. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.