Substories are short, self-contained narratives that Ichiban can undertake for the citizens of Hawaii. They often involve helping people with their problems, solving local mysteries, or dealing with petty criminals. Completing substories typically rewards you with XP, money, unique items, and sometimes even new Poundmates (summonable allies).
Look for NPCs with a '...' speech bubble above their heads on the mini-map. These indicate available substories. Some substories are multi-part and require you to return to the quest giver after completing an objective. Prioritize substories that offer bond increases for your party members, as these are invaluable for combat. There are over 50 substories scattered across Hawaii, each offering a glimpse into the lives of its inhabitants.