Lots of fantasy stories revolve around characters going on a quest. In 'Lord of the Rings', Frodo and the Fellowship were charged with returning the One Ring to its original location and destroy it. They were trying to stop a force of evil larger than anyone could have imagined. And Aragorn needed to be returned to his rightful place as the King of Men.
Most quests involve a magical item or the return of something the world thought was lost. Like the unassuming farm boy who is actually the rightful heir to a long lost throne. Perhaps it is a quest to slay a dragon and return to a city that was lost.
When starting out on a quest, there has to be some questions answered. Who is going? How will you get there? And where did you find that magical map/weapon/thing? Artifacts in fantasy quests are just as important as anything else. Some trinket is always turning up in the most unexpected places. Perhaps the key to the city of gold was tucked away in a strongbox down in some wine cellar of a farmer who retired from the military after the last battle of some now forgotten city. The only way it was found was because of the man's passing and his handing his small fortune down to a son who had to fight off greedy relatives who thought the man had other treasures hidden.
Well, they'd be right, but they certainly wouldn't know it. Not until someone else came along with a map to said city and a picture of what the key looks like.
But quests don't have to be about items or lost kings all the time. Quests can be simply finding answers to questions that have plagued a person their entire life and they finally decide to go looking for answers. Maybe the quest is to regain a freedom from a centuries old oppression. Or perhaps the person beginning the quest just wants to find out who they really are and what the fates have in store for them.