Sub Quest
Sub Quest besides the Main Quest may occur.-Sign
Indicates "Sub Quest [Accept]".
Sub Quest can be accepted.
Indicates "Sub Quest [Ongoing]".
Quest is progressed by defeating enemy, talking to certain character, etc.
Indicates "Sub Quest [Finished]".
Sub Quest can be cleared.
Indicates "Cannot be accepted".
It can be accepted by raising your level, clearing other Quests, etc.
Make sure you always check the map.