Interludes are one-time events that unlock when a Servant you own has reached a certain Bond level and has been ascended to a certain point. If the interlude takes place outside of Chaldea Gate, you must have completed the storyline of that area in order to access the interlude. Interludes can only be completed once, but visual novel scenes can be replayed from My Room.
Interludes can be found in the quest zones where they take place, regardless of whether you are eligible to attempt the quest or not. On the main hub screen, the number on the zone banner includes all interludes, locked and unlocked. However, there is a special Interlude banner under all the zone banners that will only link to unlocked Interludes.