What are quest and how do you do them?

Quests are part of the storyline. You pick them up from the boards in the center of the towns and carry them out through adventuring and fighting or finding certain items. Completing major quests gives you access to newer and more difficult areas, new zones on the map, and special gear.
I hope I'm correct in this. Jinxie took you through a tutorial on quests early on, if I remember right.

thanks