A feature brought back to 4 Ultimate, subquests are mini-quests within the quest you are embarking on that have their own smaller cash reward and material reward pool. They can range from anything to slaying a certain number of specific small minions to breaking the certain part of a large monster. If you can, you should always target to complete the subquest along with the main quest for additional money and materials. Check Quest Info when out in the area from the menu to see the subquest. When selecting quests from the Guildmarm, subquests will be displayed below the main objective.
Additionally, if you complete the subquest, you can go to the menu and select the End Via Subquest option. This will only give you the subquest’s monetary and material reward but it is a great way to either speed farm a particular quest for a particular material, or bail out early if the hunt isn’t going well so that you don’t outright fail.