Interludes are one-time events that unlock when a Servant you own has reached a specific bond level and ascension. If the interlude takes place outside of Chaldea Gate, you must have completed the story for that location in order to access the interlude. Interludes can only be completed once, but visual novel scenes can be replayed from My Room.
Interludes are found in the quest zones where they take place for all Servants you own, regardless of whether you are eligible for the interlude or not. On the main screen, the number on the zone banner includes all interludes. There is also an Interlude banner within Chaldea Gate that will link to all interludes, locked and unlocked.
As of Camelot, new interludes generally do not require any story completion and can simply be accessed from Chaldea Gate.