NPC Quests
Talking to NPCs around an island (press E) gives out quests.
Confirmed by an in-game tutorial tooltip in the official gameplay trailer: "To progress you can finish quests from NPCs around the island. Try talking to one by pressing [E] when looking at one to see what they want." Matches the multiple NPC side-quest achievements (Who stole my beer, Dinnertime, Vacation, Terrorizing bird, Deadliest catch).