From the game's encyclopedia
A Dynasty is a group of Noble descendants of a Landed ancestor; the founder of the Dynasty. The original House can split into new ones (Cadet Branches), all still members of the wider Dynasty.
When your Character dies, you must have a Player Heir, or the game will end (though you can pick another ruler and continue playing in the same world).
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.
Dynasty is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Dynasty is a group of Noble descendants of a Landed ancestor; the founder of the Dynasty." It covers Dynasty Head and Denounce. The game also links it as Dynasties and Dynasty Members. 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.