Your world doesn't stand still between conversations. Here's what moves on its own, and how to steer it.
While you're out on the map, the clock runs. A full in-game day takes about a quarter of an hour of real time.
It pauses on its own while you're in a conversation, in the Atlas, in a battle or in Build mode, and after a few minutes without any input. Choose Live / Paused on the Command Deck to stop it yourself.
Conversations move time along too: each reply advances the clock by however long it would take to say.
The day has eight parts, from Dawn to Night. A new day begins at dawn, not at midnight. Time only passes while your world is open, so closing the game freezes it. See Time and days.
As the day moves through its parts, the people around you go about their routines:
Some take the occasional day off. Trips you've scheduled for someone take them across the map and back, and a banner lets you know when they set off.
When people share a building, they meet and talk among themselves, and news passes from one to the next as gossip. Someone you've never met may have already heard about you.
You set each character's home, workplace, favorite places, days off and trips on their profile. See NPC daily life.
When a new day begins:
Notes you add in Journal → World steer what the digest writes. See Overnight.
Each day, a few buildings in the settlement you're in get a blue marker. Someone inside is in the middle of something. Walk in and they'll draw you into it. Story Moments are part of the paid plans. See Story Moments.
Journal → Preferences lets you steer the kinds of stories you get. See Story preferences.
The Journal (the open-book icon) is where all of this shows up: your notes, the day cards and Story So Far, everyone you've met and what they remember, and your story preferences. See Memory and the Journal.