Even quests are classified in levels.
Quests are classified in levels from 1 to 10 based on their degree of difficulty. Generally the higher the level of the quest, the better the reward and the amount of EXP points gains.
Other than defeating monsters to make yourself stronger, you can choose to work on quests to earn a decent amount of EXP by completing a quest. You will also earn mesos and rare items along the way.
There are a number of quests that will be unavailable if you miss the opportunity to do it. So try to talk to as many NPCs as possible during your journey to take advantage of as many quests as possible.
