From the game's encyclopedia
Characters of most Faiths can choose to undertake an Activity to go on a Pilgrimage to a Holy Site. Each Holy Site has an individual grace period before you can revisit.
Such a journey may be filled with both opportunity and peril, but upon reaching their destination characters will earn Piety and may receive other rewards.
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.
Pilgrimage is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "Characters of most Faiths can choose to undertake an Activity to go on a Pilgrimage to a Holy Site." The game also links it as Pilgrimages. 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.