This game mechanic is where events happen within the game depending on a specific circumstance. A popular way this mechanic is used is by having time events where certain things happen depending on the time set on your computer or console.
A good example is in Lord of The Rings Online. At popular holidays in the year such as Easter, Halloween, and Christmas there will be a festival where the players can complete unique quests which are only available at that time of year and collect rewards that show they were from that festival, For example, a pumpkin helmet to show Halloween.
The Forza franchise also uses this mechanic in the form of rival races. When the player drives through certain areas of the map they will see other racers speed past which trigger a race with them. This can happen in random places and does not always depend on the time.
I would use this mechanic similarly to how LOTRO uses it which is to have events in te game that happen on popular holidays. The reason I would do this is because it would mean that the players know when the events are happening.